{"cells":[{"cell_type":"markdown","metadata":{"_id":"76F4D98782D3445881BBC502F7948326","id":"C93236FB44CF4475A8D1407FC9116A91","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["# <center>高级心理统计 (Advanced Statistics in Psych Sci) </center>  \n","## <center>《贝叶斯统计及其在Python中的实现》 (Bayesian inference with Python) </center>  \n","## <center>Instructor： 胡传鹏（博士）(Dr. Hu Chuan-Peng) </center>  \n","### <center>南京师范大学心理学院 (School of Psychology, Nanjing Normal University)  </center>"]},{"cell_type":"markdown","metadata":{"_id":"0C8CF2C2C5AE4DD5AC61D1958C3E9AC6","id":"260AB14A8B684568A777CA9C2F4368E0","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["## <center> Part 1: Why Bayesian statistics  </center>"]},{"cell_type":"markdown","metadata":{"_id":"AE2385E248EB41A981098425904C6A82","id":"E519B28EB81E47BC9660729ECA84E667","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["<center>  \n","\t研究人类心理与行为的规律，容易吗？  \n","</center>"]},{"cell_type":"markdown","metadata":{"_id":"B2DAB9A514D64A1686941A3EF2CB09DC","id":"833DB60A28B745AEA7A78FD898147E0A","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["## Outlines  \n","* 1. 为什么要学习本课程 [Why Bayesia inference]  \n","* 2. 本课程的内容将是什么 [What is the syllabus]  \n","* 3. 如何学好这门课[How can I learn this course well]"]},{"cell_type":"markdown","metadata":{"_id":"A90D0E61CDF047958FA969DC43CB941A","id":"035127B7D9A54BD1A7E3B8CCD3ECC42F","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["##  1. 为什么要学习本课程 (Why Bayesia inference)  \n","\n","### 1.1 为什么心理学需要更好的方法 (Why does psychological science need better methods?)  \n","\n","#### 原因1: 人类认知与行为本身的复杂性"]},{"cell_type":"markdown","metadata":{"_id":"D2F8C116B35A4F66B4768B81EB00E6E9","id":"A1626156613C450987B9A3FC71824ED2","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["![Image Name](https://cdn.kesci.com/upload/image/rhdcyu860w.gif?imageView2/0/w/960/h/960)  \n","\n","\n","Source: https://www.science.org/toc/science/309/5731"]},{"cell_type":"markdown","metadata":{"_id":"3B0BFDA39AB54194836801382E065EC3","id":"4EBE5C2ACDCF49269BF03146952CEEFC","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["**Q1: What is the Uiverse Made of (physics)**  \n","\n","**Q2: What is the Biological Basis of Consciouness (psychological/cognitive science)**"]},{"cell_type":"markdown","metadata":{"_id":"725F3E2FFF5A41229219B57BD0098E8B","id":"59E4EC96662C433F89A7914D727698A0","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["##### Q:  \n","重要性和复杂度相似的问题，是否意味着研究方法也应该类似地复杂？"]},{"cell_type":"markdown","metadata":{"_id":"1DF072C580954817A7CEF5F472B4327B","id":"A635B26CF98B4AB59E5E2E486AE4D262","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["##### 物理学中的方法 (Methods in Physics):  \n","\n","Example 1: Webb telescope (韦伯望远镜)  (**equipment**)"]},{"cell_type":"markdown","metadata":{"_id":"EF5620DDBB7546239301A44A2D028CF5","id":"949DF3E8A7D24C97B79CC05A7FDDF320","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["\n","![Image Name](https://cdn.kesci.com/upload/image/rhdd0r46k3.png?imageView2/0/w/720/h/640)  \n"]},{"cell_type":"markdown","metadata":{"_id":"5EFA52B2722A40E1A0A3B9BB3D72363A","id":"CBBBAF9100EC41409016FD2B6D508586","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["Example 2: Big-team science (CERN, the European Organization for Nuclear Research) ---- **equipment & practices**  \n","\n","Example 3: **Mathematics**"]},{"cell_type":"markdown","metadata":{"_id":"FE0863A20CCD456084484A5CE23F61E6","id":"54ED0E99CA074A5B88401A2E6816EA07","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["##### 其他研究人类智能的领域所采用的方法 (Methods in other fields that also study \"intelligence\")  \n","\n","**AI**  \n","\n","\n","![Image Name](https://cdn.kesci.com/upload/image/rhdd1sr5y2.png?imageView2/0/w/640/h/640)  \n"]},{"cell_type":"markdown","metadata":{"_id":"A698E36FE0044D579A17CA8A78BDDC33","id":"F8DD0D89247D417C90BE653F562F35F2","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["##### 心理科学的研究方法 [What do psychological scientists have?]  \n","你们能够想到的研究方法包括哪些？"]},{"cell_type":"markdown","metadata":{"_id":"C3F1598B01734C308FEE84A0C49A0481","id":"9249F6C8E9ED4A758BE7958AE7BA2F6A","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["\n","![Image Name](https://cdn.kesci.com/upload/image/rhdd2dgwc8.png?imageView2/0/w/640/h/640)  \n"]},{"cell_type":"markdown","metadata":{"_id":"264CCEA515364AEC8A148284221E248F","id":"94A597F7032449C59B9A7A02B9BB7943","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["**实证研究：**  \n","* 质性研究  \n","* 观察法  \n","* 问卷  \n","* 行为实验  \n","* 眼动、生理数据记录  \n","* EEG/ERP/MEG  \n","* fMRI/PET/fNIRs  \n","* TMS/tDCS  \n","* ..."]},{"cell_type":"markdown","metadata":{"_id":"9A01943A25CE4414A077DBA256AA1DA8","id":"E50067700872437A98BA698072B3C3B9","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["**统计方法：**  \n","* t-test  \n","* ANOVA  \n","* Correlation  \n","* Structural equation model (SEM)  \n","* ?"]},{"cell_type":"markdown","metadata":{"_id":"320FCB224BDA47E495E08922E3741EA1","id":"B6882469C0CE4D519C3895F8CA30E437","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["##### 相关方法课程：  \n","* 心理测量  \n","* 心理统计（包括SPSS等）  \n","* 实验心理学（包括E-prime等）  \n","* ？"]},{"cell_type":"markdown","metadata":{"_id":"56D804D678A641C898763573572B9FCB","id":"47A02AAF181247438548BAE10CC8F119","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["* 更好的仪器  \n","* **更好的统计/数据分析**  \n","* 更好的实践 (e.g., big-team science)"]},{"cell_type":"markdown","metadata":{"_id":"CD553C169C78422B8E82077F709EA240","id":"A7E1883A950E4F51BC811657D6181205","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["#### 原因2: 更复杂的数据  \n","\n","* 数据字化的时代，大数据  \n","* 神经成像/生理数据  \n","* 多模态的数据融合"]},{"cell_type":"markdown","metadata":{"_id":"B2C8043BCAF5439A84683A99970C683F","id":"482419651A6A483C9E00DD524D9FCBF1","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["### 1.2 确实有更好的统计方法"]},{"cell_type":"markdown","metadata":{"_id":"1ACA3D17ECDE49608846C08EB60F4B3D","id":"385B8D7795784FDE8EDC908D7DBAFCAC","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["**贝叶斯统计 (Bayesian inference)  **  \n","\n","\n","![Image Name](https://cdn.kesci.com/upload/image/rhdf3bb12c.png?imageView2/0/w/640/h/640)  \n","\n"]},{"cell_type":"markdown","metadata":{"_id":"95DD8C33EE804FAF8B97A4CBC101E342","id":"6B465873C1874D6BBDE1E851D63C0DD0","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["* 灵活/强大/能用  \n","* 易用  \n","* 可拓展性强  \n","* 方便跨学科交流  \n","* ..."]},{"cell_type":"markdown","metadata":{"_id":"A7EDD67105744B03869FFF04B039DA6C","id":"A89D649228C04623806E13985C924861","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["##### 灵活/强大/通用  \n","\n","不需要解析解  \n","\n","贝叶斯分析在多个学科中得到广泛应用，尤其是AI。"]},{"cell_type":"markdown","metadata":{"_id":"6AF6B87DEECD421C8EA19C8E65DC5C03","id":"834D7DD301BD42CC976B8C3776C88C18","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["##### （相对）易用  \n","\n","概率编程语言(Probabilistic Programming Languages)的发展和普及  \n","\n","\n","PPLs: *computational languages for statistical modeling*  \n","\n","* PyMC  \n","* Stan  \n","* NumPyro  \n","* Pyro  \n","* BUGS  \n","* ..."]},{"cell_type":"markdown","metadata":{"_id":"7F08D5B0BD39457583616DA28E3271F0","id":"CC729E9C75B7469FA3E8605E8B7BABEF","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["大部分情况下，开发者使用它可以轻松地定义概率模型，然后程序会自动地求解模型。  \n","\n","\n","![Image Name](https://cdn.kesci.com/upload/image/rhdf4r9fbh.png?imageView2/0/w/640/h/640)  \n","\n","\n","Source: https://towardsdatascience.com/intro-to-probabilistic-programming-b47c4e926ec5  \n"]},{"cell_type":"markdown","metadata":{"_id":"5C626AB2718D49578D7F8B2B0EA25B5C","id":"4EEF782716F143FEAB9C1AB36EF3445A","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["##### 可拓展  \n","\n","贝叶斯概念已经应用到以深度学习为中心的新技术的发展，包括深度学习框架(TensorFlow, Pytorch)，创建表示能力更强、数据驱动的模型"]},{"cell_type":"markdown","metadata":{"_id":"110133AA82664BECA136B94A31D6E355","id":"428A23E1F297499AA56B9488E5CCAE2E","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["##### 方便交流  \n","大部分PPLs都有类似的数据结构，但是不同的学科使用的语言不同。  \n","\n","心理学/社会科学/神经科学：  \n","* **PyMC3**  \n","* Stan  \n","* BUGS"]},{"cell_type":"markdown","metadata":{"_id":"48D23201C57940BEA41475A298B4A201","id":"CDA05DE3AD8F4ACCBC35837A9283E05B","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["<div style=\"text-align: center;\">\t \n","\t\n","## Part 2: Two examples  \n","\t\n","</div> "]},{"cell_type":"markdown","metadata":{"_id":"CBCA0A62808F48F4B9C37BBF9847021F","id":"A429C54535F84864839CA37D6E7F4498","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["### 例1：社会关系地位与幸福感的关系  \n","\n","实例的数据来自[ Many Labs 2 项目](osf.io/uazdm/)中的一个研究。  \n","\n","该研究探究了社会关系地位对于幸福感的影响 “Sociometric status and well-being”， (Anderson, Kraus, Galinsky, & Keltner, 2012)。  \n","\n","该数据集包括6905个被试的数据。"]},{"cell_type":"code","execution_count":1,"metadata":{"_id":"2738299CA3B4440D9779992A31E46998","collapsed":false,"id":"700B687940164DFF891599310FAD2D64","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","scrolled":true,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[],"source":["# import modules\n","import arviz as az\n","import matplotlib.pyplot as plt\n","import numpy as np\n","import pandas as pd\n","import pymc as pm\n","import xarray as xr\n","\n","%config InlineBackend.figure_format = 'retina'\n","az.style.use(\"arviz-darkgrid\")\n","rng = np.random.default_rng(1234)\n","\n","import matplotlib\n","matplotlib.rcParams['figure.figsize'] = [4, 3]"]},{"cell_type":"code","execution_count":2,"metadata":{"_id":"179B5A9513CC48DF8A29708C1EE0C352","collapsed":false,"id":"495A808C5A5B44AAB4956B12BD5AFC66","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","scrolled":true,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[],"source":["# 导入数据, 注意在和鲸和在自己电脑（本地）时有差异）\n","try:\n","  SMS_data = pd.read_csv('/home/mw/input/Bayesian3285/data_chp1_SMS_Well_being.csv')\n","except:\n","  SMS_data = pd.read_csv('data/data_chp1_SMS_Well_being.csv')\n","SMS_data = SMS_data[['uID','variable','factor','Country']]\n","# 把数据分为高低两种社会关系的地位的子数据以便画图与后续分析\n","plot_data = [\n","    sorted(SMS_data.query('factor==\"Low\"').variable[0:3000]),\n","    sorted(SMS_data.query('factor==\"High\"').variable[0:3000])]"]},{"cell_type":"markdown","metadata":{"_id":"0DCF70157B23491085EBCC847D54934D","id":"89EB1A73012048E0B61E2C86ED738AA4","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["#### 通过画图对于两种社会关系地位对幸福感的影响  \n","\n","图中横坐标代表高低两种社会关系地位，纵坐标代表了主观幸福感评分。"]},{"cell_type":"code","execution_count":3,"metadata":{"_id":"6AD2473435164EDA8071FBED8128A31D","collapsed":false,"id":"795994958F5441F7B6784F9C08A68BFD","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[],"source":["# import matplotlib\n","# a = sorted([f.name for f in matplotlib.font_manager.fontManager.ttflist])\n","\n","# for i in a:\n","#    print(i)\n","\n","# 字体样式\n","font = {'family' : 'Source Han Sans CN'}\n","# 具体使用\n","plt.rc('font',**font)"]},{"cell_type":"code","execution_count":4,"metadata":{"_id":"DBD1ED67F52F4A43A5A05002B23C37AB","collapsed":false,"id":"B1DDDBC6D6434FD69B04E84A13CF1017","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[{"data":{"text/html":["<img src=\"https://cdn.kesci.com/upload/rt/B1DDDBC6D6434FD69B04E84A13CF1017/s1403hy16k.png\">"],"text/plain":["<Figure size 900x400 with 1 Axes>"]},"metadata":{"image/png":{"height":411,"width":911}},"output_type":"display_data"}],"source":["# 画图对比两种社会地位对幸福感的影响\n","def adjacent_values(vals, q1, q3):\n","    upper_adjacent_value = q3 + (q3 - q1) * 1.5\n","    upper_adjacent_value = np.clip(upper_adjacent_value, q3, vals[-1])\n","\n","    lower_adjacent_value = q1 - (q3 - q1) * 1.5\n","    lower_adjacent_value = np.clip(lower_adjacent_value, vals[0], q1)\n","    return lower_adjacent_value, upper_adjacent_value\n","\n","def set_axis_style(ax, labels):\n","    ax.xaxis.set_tick_params(direction='out')\n","    ax.xaxis.set_ticks_position('bottom')\n","    ax.set_xticks(np.arange(1, len(labels) + 1), labels=labels)\n","    ax.set_xlim(0.25, len(labels) + 0.75)\n","    ax.set_xlabel('社会关系地位')\n","\n","fig, ax1 = plt.subplots(nrows=1, ncols=1, figsize=(9, 4), sharey=True)\n","\n","parts = ax1.violinplot(\n","        plot_data, showmeans=False, showmedians=False,\n","        showextrema=False)\n","\n","for pc in parts['bodies']:\n","    pc.set_facecolor('#D43F3A')\n","    pc.set_edgecolor('black')\n","    pc.set_alpha(1)\n","\n","quartile1, medians, quartile3 = np.percentile(plot_data, [25, 50, 75], axis=1)\n","whiskers = np.array([\n","    adjacent_values(sorted_array, q1, q3)\n","    for sorted_array, q1, q3 in zip(plot_data, quartile1, quartile3)])\n","whiskers_min, whiskers_max = whiskers[:, 0], whiskers[:, 1]\n","\n","inds = np.arange(1, len(medians) + 1)\n","ax1.scatter(inds, medians, marker='o', color='white', s=30, zorder=3)\n","ax1.vlines(inds, quartile1, quartile3, color='k', linestyle='-', lw=5)\n","ax1.vlines(inds, whiskers_min, whiskers_max, color='k', linestyle='-', lw=1)\n","\n","# set style for the axes\n","labels = ['低','高']\n","plt.xticks(np.arange(2)+1, labels)\n","plt.xlabel('社会关系地位')\n","plt.ylabel('幸福感')\n","\n","plt.show()"]},{"cell_type":"markdown","metadata":{"_id":"D4177BAEA2D045A48671D6F4D62B8709","id":"0FE977D8FB7142749C81F8B873378F85","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["#### 通过*t*检验，分析两种社会关系地位下幸福感的差异  \n","\n","结果发现，两种社会关系水平下被试的主观幸福感边缘显著，*t*(6903) = -1.76, *p* = .08。"]},{"cell_type":"code","execution_count":5,"metadata":{"_id":"CA6DF4FAE8C04CA282F7D9AA98CFED12","collapsed":false,"id":"B2F383EF1B5F4B0A9049924A6A9F558F","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[{"name":"stdout","output_type":"stream","text":["低社会关系：0.014 ± 0.66； 高社会关系：-0.014 ± 0.67\n"]},{"data":{"text/plain":["TtestResult(statistic=1.7593310889762195, pvalue=0.07856558333862036, df=6903.0)"]},"execution_count":5,"metadata":{},"output_type":"execute_result"}],"source":["from scipy import stats\n","SMS_low = SMS_data.query('factor==\"Low\"').variable.values\n","SMS_high = SMS_data.query('factor==\"High\"').variable.values\n","print(\n","    f\"低社会关系：{np.around(np.mean(SMS_low),3)} ± {np.around(np.std(SMS_low),2)}；\",\n","    f\"高社会关系：{np.around(np.mean(SMS_high),3)} ± {np.around(np.std(SMS_high),2)}\")\n","    \n","stats.ttest_ind(\n","    a= SMS_low,\n","    b= SMS_high, \n","    equal_var=True)"]},{"cell_type":"markdown","metadata":{"_id":"25A7B86CB2E54F459CBA5388680895F2","id":"C18E7C5F1A434F818C2C0402F29708B6","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["#### 通过贝叶斯推断替代*t*检验  \n","\n","零假设显著性检验（Null hypothesis significance test, NHST）的框架之下，*t*检验只提供了一个二分的结果：拒绝或者无法拒绝$H_0$。 但 *p* = 0.078这样的结果无法支持$H_0$  \n","\n","贝叶斯推断是否可以带来不一样的结果？  \n","\n","一个简单的线性模型：  \n","\n","1. 通过建立线性模型去替代原本的*t*检验模型。  \n","\n","2. 通过PyMC对后验进行采样  \n","\n","3. 通过Arviz对结果进行展示，辅助统计推断"]},{"cell_type":"code","execution_count":6,"metadata":{"_id":"0E201A12425844FE8CADDB483A25D258","collapsed":false,"id":"0E8AC6886FAC42698BF0E64B1705DFAF","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[],"source":["# 通过pymc建立基于贝叶斯的线性模型\n","x = pd.factorize(SMS_data.factor)[0] # high为0，low为1\n","\n","with pm.Model() as linear_regression:\n","    sigma = pm.HalfCauchy(\"sigma\", beta=2)\n","    beta0 = pm.Normal(\"beta0\", 0, sigma=5)\n","    beta1 = pm.Normal(\"beta1\", 0, sigma=5)\n","    x = pm.MutableData(\"x\", x)\n","    # μ = pm.Deterministic(\"μ\", β0 + β1 * x)\n","    pm.Normal(\"y\", mu=beta0 + beta1 * x, sigma=sigma, observed=SMS_data.variable)"]},{"cell_type":"markdown","metadata":{"_id":"47219BB0581C4A6F809EDD07409F9C28","id":"E5A253D1CAC64F57B2243C139D721276","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["可以通过pymc自带的可视化工具将模型关系可视化。  \n","\n","x 为自变量，其中1为低社会关系，0为高社会关系。  \n","\n","参数 $\\beta0$ 是线性模型的截距，而 $\\beta1$ 是斜率。  \n","\n","截距代表了高社会关系地位被试的幸福感；而截距加上斜率表示低社会关系地位被试的幸福感。  \n","\n","参数$sigma$是残差，因变量$y$即主观幸福感。  \n","\n","模型图展示了各参数通过怎样的关系影响到因变量。"]},{"cell_type":"code","execution_count":7,"metadata":{"_id":"F325634DE8AD46D1B0120EAC7B1FCCBA","collapsed":false,"id":"FDC10165AF4945AF9CBF97825D065347","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","scrolled":true,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[{"data":{"text/html":["<img src=\"https://cdn.kesci.com/upload/rt/FDC10165AF4945AF9CBF97825D065347/s1403i833i.svg\">"],"text/plain":["<graphviz.graphs.Digraph at 0x7f23b64d36d0>"]},"execution_count":7,"metadata":{},"output_type":"execute_result"}],"source":["pm.model_to_graphviz(linear_regression)"]},{"cell_type":"code","execution_count":8,"metadata":{"_id":"72D1FA46ECAB40F78C5DADA7225D3A93","collapsed":false,"id":"00A05CB8B975450C854DA33D81E054E7","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[{"name":"stderr","output_type":"stream","text":["Auto-assigning NUTS sampler...\n","Initializing NUTS using jitter+adapt_diag...\n","Multiprocess sampling (4 chains in 4 jobs)\n","NUTS: [sigma, beta0, beta1]\n"]},{"data":{"text/html":["\n","<style>\n","    /* Turns off some styling */\n","    progress {\n","        /* gets rid of default border in Firefox and Opera. */\n","        border: none;\n","        /* Needs to be in here for Safari polyfill so background images work as expected. */\n","        background-size: auto;\n","    }\n","    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n","        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n","    }\n","    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n","        background: #F44336;\n","    }\n","</style>\n"],"text/plain":["<IPython.core.display.HTML object>"]},"metadata":{},"output_type":"display_data"},{"name":"stderr","output_type":"stream","text":["Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 23 seconds.\n"]}],"source":["# 模型拟合过程 (mcmc采样过程)\n","with linear_regression:\n","    idata = pm.sample(2000, tune=1000, target_accept=0.9, return_inferencedata=True)"]},{"cell_type":"markdown","metadata":{"_id":"3F0AAA3A23D0470E96DD8816F6B0C811","id":"3652D18D7FBA4E939856725E2CCC6F9A","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["#### 参数的后验分布  \n","这里的模型分析结果展示了各参数的分布(后验)情况"]},{"cell_type":"code","execution_count":9,"metadata":{"_id":"48F96E7CA7B94E0CA215E3D0400E66F2","collapsed":false,"id":"B41FE0F838614075A59F0E0A167E497F","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[{"data":{"text/html":["<img src=\"https://cdn.kesci.com/upload/rt/B41FE0F838614075A59F0E0A167E497F/s1405qw11h.png\">"],"text/plain":["<Figure size 1200x600 with 6 Axes>"]},"metadata":{"image/png":{"height":611,"width":1211}},"output_type":"display_data"}],"source":["az.plot_trace(idata);"]},{"cell_type":"markdown","metadata":{"_id":"733936FB22BE43A3AA687E3A453EAA14","id":"740D52C263A348DC97FD525B3751B011","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["下图反应了参数β1的可信度，即两个社会关系下幸福感差异的可信度。  \n","\n","结果显示，两个社会关系下幸福感差异的可信度为96%。"]},{"cell_type":"code","execution_count":10,"metadata":{"_id":"4BC6A75D108040D98218CF56895FB22C","collapsed":false,"id":"CBE17AD0B936450293495771C4644571","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[{"data":{"text/plain":["array(0.96075)"]},"execution_count":10,"metadata":{},"output_type":"execute_result"}],"source":["(idata.posterior.beta1 > 0).mean().values"]},{"cell_type":"code","execution_count":11,"metadata":{"_id":"2F3E4E9927C445EA83E9FF4EA3CC2B6A","collapsed":false,"id":"55399EEFCE1E4603A737835B5B4A53EE","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[{"data":{"text/html":["<img src=\"https://cdn.kesci.com/upload/rt/55399EEFCE1E4603A737835B5B4A53EE/s1405qkchx.png\">"],"text/plain":["<Figure size 400x300 with 1 Axes>"]},"metadata":{"image/png":{"height":311,"width":411}},"output_type":"display_data"}],"source":["axes = az.plot_posterior(idata, var_names=['beta1'], kind='hist',ref_val=0)"]},{"cell_type":"code","execution_count":12,"metadata":{"_id":"251F81E217604FE789A51FA9D3446077","collapsed":false,"id":"16B3BE6BE96244C599983A280A0CFDAB","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[{"data":{"text/html":["<img src=\"https://cdn.kesci.com/upload/rt/16B3BE6BE96244C599983A280A0CFDAB/s1405q4yai.png\">"],"text/plain":["<Figure size 400x300 with 1 Axes>"]},"metadata":{"image/png":{"height":311,"width":411}},"output_type":"display_data"}],"source":["axes = az.plot_posterior(idata, var_names=['beta1'], kind='hist', rope = [-0.1, 0.1], hdi_prob=.95)"]},{"cell_type":"markdown","metadata":{"_id":"2FAB7701C48B412582AE5FCB488FCF69","id":"24D335154FAA4D58971FF476F93B05E0","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["#### 模型诊断  \n","\n","通过模型思维进行数据分析需要注意模型检验，即检验模型是否能有效的反应数据的特征。"]},{"cell_type":"markdown","metadata":{"_id":"33337DB7DE92428E836926A1C5AC59EB","id":"0306DFD7C93340028756EC4FB0DAD5FE","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["下表格为模型参数的基本信息：  \n","\n","mean和sd 为各参数的均值和标准差；  \n","hdi 3%-97% 为参数分布的可信区间；  \n","msce mean和sd 为mcmc采样标准误统计量的均值和标准差；  \n","ess bulk和tail 反应了mcmc采样有效样本数量相关性能；  \n","r hat 为参数收敛性的指标。"]},{"cell_type":"code","execution_count":13,"metadata":{"_id":"BF9087B69C4D48518559EF54E1F52552","collapsed":false,"id":"ED567266D9F944D3B877F26A8928AF89","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[{"data":{"text/html":["<div>\n","<style scoped>\n","    .dataframe tbody tr th:only-of-type {\n","        vertical-align: middle;\n","    }\n","\n","    .dataframe tbody tr th {\n","        vertical-align: top;\n","    }\n","\n","    .dataframe thead th {\n","        text-align: right;\n","    }\n","</style>\n","<table border=\"1\" class=\"dataframe\">\n","  <thead>\n","    <tr style=\"text-align: right;\">\n","      <th></th>\n","      <th>mean</th>\n","      <th>sd</th>\n","      <th>hdi_3%</th>\n","      <th>hdi_97%</th>\n","      <th>mcse_mean</th>\n","      <th>mcse_sd</th>\n","      <th>ess_bulk</th>\n","      <th>ess_tail</th>\n","      <th>r_hat</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>beta0</th>\n","      <td>-0.014</td>\n","      <td>0.011</td>\n","      <td>-0.035</td>\n","      <td>0.008</td>\n","      <td>0.0</td>\n","      <td>0.0</td>\n","      <td>4850.0</td>\n","      <td>4966.0</td>\n","      <td>1.0</td>\n","    </tr>\n","    <tr>\n","      <th>beta1</th>\n","      <td>0.028</td>\n","      <td>0.016</td>\n","      <td>-0.002</td>\n","      <td>0.057</td>\n","      <td>0.0</td>\n","      <td>0.0</td>\n","      <td>5038.0</td>\n","      <td>5125.0</td>\n","      <td>1.0</td>\n","    </tr>\n","    <tr>\n","      <th>sigma</th>\n","      <td>0.661</td>\n","      <td>0.006</td>\n","      <td>0.650</td>\n","      <td>0.671</td>\n","      <td>0.0</td>\n","      <td>0.0</td>\n","      <td>5129.0</td>\n","      <td>5513.0</td>\n","      <td>1.0</td>\n","    </tr>\n","  </tbody>\n","</table>\n","</div>"],"text/plain":["        mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n","beta0 -0.014  0.011  -0.035    0.008        0.0      0.0    4850.0    4966.0   \n","beta1  0.028  0.016  -0.002    0.057        0.0      0.0    5038.0    5125.0   \n","sigma  0.661  0.006   0.650    0.671        0.0      0.0    5129.0    5513.0   \n","\n","       r_hat  \n","beta0    1.0  \n","beta1    1.0  \n","sigma    1.0  "]},"execution_count":13,"metadata":{},"output_type":"execute_result"}],"source":["az.summary(idata)"]},{"cell_type":"markdown","metadata":{"_id":"E401849648344D3F95097A5DDE5DDE50","id":"F67FD257F2CD43E987DCC23F799FD8BF","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["### 后验预测检验 ppc (posterior predictive check)"]},{"cell_type":"code","execution_count":14,"metadata":{"_id":"05594867D7C04975B1B681D9E08F3494","collapsed":false,"id":"89495C7959B64A5B80096AF35FED8FE6","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","scrolled":true,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[{"name":"stderr","output_type":"stream","text":["Sampling: [y]\n"]},{"data":{"text/html":["\n","<style>\n","    /* Turns off some styling */\n","    progress {\n","        /* gets rid of default border in Firefox and Opera. */\n","        border: none;\n","        /* Needs to be in here for Safari polyfill so background images work as expected. */\n","        background-size: auto;\n","    }\n","    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n","        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n","    }\n","    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n","        background: #F44336;\n","    }\n","</style>\n"],"text/plain":["<IPython.core.display.HTML object>"]},"metadata":{},"output_type":"display_data"}],"source":["x,x_levels = SMS_data.factor.factorize()\n","\n","with linear_regression:\n","    pm.set_data({\"x\": x})\n","    idata_ppc = pm.sample_posterior_predictive(\n","        idata, \n","        var_names=[\"y\"],\n","        return_inferencedata=True,\n","        predictions=True,\n","        extend_inferencedata=True\n",")"]},{"cell_type":"code","execution_count":15,"metadata":{"collapsed":false,"id":"6A43F01A5C7B46C488786CE9070A9E74","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[{"data":{"text/html":["\n","            <div>\n","              <div class='xr-header'>\n","                <div class=\"xr-obj-type\">arviz.InferenceData</div>\n","              </div>\n","              <ul class=\"xr-sections group-sections\">\n","              \n","            <li class = \"xr-section-item\">\n","                  <input id=\"idata_posterior7af277a5-30cd-449b-ab95-426db779e130\" class=\"xr-section-summary-in\" type=\"checkbox\">\n","                  <label for=\"idata_posterior7af277a5-30cd-449b-ab95-426db779e130\" class = \"xr-section-summary\">posterior</label>\n","                  <div class=\"xr-section-inline-details\"></div>\n","                  <div class=\"xr-section-details\">\n","                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n","                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n","<defs>\n","<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n","<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n","<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n","<path d=\"M16 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1z\"></path>\n","</symbol>\n","</defs>\n","</svg>\n","<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n"," *\n"," */\n","\n",":root {\n","  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n","  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n","  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n","  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n","  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n","  --xr-background-color: var(--jp-layout-color0, white);\n","  --xr-background-color-row-even: var(--jp-layout-color1, white);\n","  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n","}\n","\n","html[theme=dark],\n","body[data-theme=dark],\n","body.vscode-dark {\n","  --xr-font-color0: rgba(255, 255, 255, 1);\n","  --xr-font-color2: rgba(255, 255, 255, 0.54);\n","  --xr-font-color3: rgba(255, 255, 255, 0.38);\n","  --xr-border-color: #1F1F1F;\n","  --xr-disabled-color: 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width: auto;\n","  z-index: 1;\n","}\n","\n",".xr-var-attrs,\n",".xr-var-data,\n",".xr-index-data {\n","  display: none;\n","  background-color: var(--xr-background-color) !important;\n","  padding-bottom: 5px !important;\n","}\n","\n",".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",".xr-var-data-in:checked ~ .xr-var-data,\n",".xr-index-data-in:checked ~ .xr-index-data {\n","  display: block;\n","}\n","\n",".xr-var-data > table {\n","  float: right;\n","}\n","\n",".xr-var-name span,\n",".xr-var-data,\n",".xr-index-name div,\n",".xr-index-data,\n",".xr-attrs {\n","  padding-left: 25px !important;\n","}\n","\n",".xr-attrs,\n",".xr-var-attrs,\n",".xr-var-data,\n",".xr-index-data {\n","  grid-column: 1 / -1;\n","}\n","\n","dl.xr-attrs {\n","  padding: 0;\n","  margin: 0;\n","  display: grid;\n","  grid-template-columns: 125px auto;\n","}\n","\n",".xr-attrs dt,\n",".xr-attrs dd {\n","  padding: 0;\n","  margin: 0;\n","  float: left;\n","  padding-right: 10px;\n","  width: auto;\n","}\n","\n",".xr-attrs dt {\n","  font-weight: normal;\n","  grid-column: 1;\n","}\n","\n",".xr-attrs dt:hover span {\n","  display: inline-block;\n","  background: var(--xr-background-color);\n","  padding-right: 10px;\n","}\n","\n",".xr-attrs dd {\n","  grid-column: 2;\n","  white-space: pre-wrap;\n","  word-break: break-all;\n","}\n","\n",".xr-icon-database,\n",".xr-icon-file-text2,\n",".xr-no-icon {\n","  display: inline-block;\n","  vertical-align: middle;\n","  width: 1em;\n","  height: 1.5em !important;\n","  stroke-width: 0;\n","  stroke: currentColor;\n","  fill: currentColor;\n","}\n","</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n","Dimensions:  (chain: 4, draw: 2000)\n","Coordinates:\n","  * chain    (chain) int64 0 1 2 3\n","  * draw     (draw) int64 0 1 2 3 4 5 6 7 ... 1993 1994 1995 1996 1997 1998 1999\n","Data variables:\n","    beta0    (chain, draw) float64 -0.02055 -0.02295 ... -0.02106 -0.01747\n","    beta1    (chain, draw) float64 0.05507 0.02629 0.03538 ... 0.007626 0.03623\n","    sigma    (chain, draw) float64 0.6614 0.6664 0.6558 ... 0.6628 0.6535 0.6634\n","Attributes:\n","    created_at:                 2023-09-17T02:55:38.498221\n","    arviz_version:              0.14.0\n","    inference_library:          pymc\n","    inference_library_version:  5.6.0\n","    sampling_time:              22.513349771499634\n","    tuning_steps:               1000</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-87e97a8c-16c7-48f5-a67b-aa9272056390' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-87e97a8c-16c7-48f5-a67b-aa9272056390' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 4</li><li><span class='xr-has-index'>draw</span>: 2000</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-bf323830-222b-44d1-8e34-edb52371d271' class='xr-section-summary-in' type='checkbox'  checked><label for='section-bf323830-222b-44d1-8e34-edb52371d271' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3</div><input id='attrs-1c7da71e-1bbe-4bfb-8e14-f322169e2dd1' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-1c7da71e-1bbe-4bfb-8e14-f322169e2dd1' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-502014a3-c127-48c1-a76f-332a641956cb' class='xr-var-data-in' type='checkbox'><label for='data-502014a3-c127-48c1-a76f-332a641956cb' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 2, 3])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 1996 1997 1998 1999</div><input id='attrs-ec5edd57-95ce-4aae-92f8-b07f51c18e28' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-ec5edd57-95ce-4aae-92f8-b07f51c18e28' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-7e7399aa-c841-454a-a9dd-ee28ec4962f2' class='xr-var-data-in' type='checkbox'><label for='data-7e7399aa-c841-454a-a9dd-ee28ec4962f2' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 1997, 1998, 1999])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-f1c74c02-b73a-49c9-885d-507df752ff76' class='xr-section-summary-in' type='checkbox'  checked><label for='section-f1c74c02-b73a-49c9-885d-507df752ff76' class='xr-section-summary' >Data variables: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>beta0</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-0.02055 -0.02295 ... -0.01747</div><input id='attrs-1131152f-9775-451a-9c47-de6be4561578' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-1131152f-9775-451a-9c47-de6be4561578' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-3025b092-49c1-4525-b68b-c08c0f7961cb' class='xr-var-data-in' type='checkbox'><label for='data-3025b092-49c1-4525-b68b-c08c0f7961cb' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[-0.02054788, -0.02294967, -0.02768306, ..., -0.02844909,\n","        -0.03099852, -0.01088267],\n","       [ 0.00218718,  0.00095151, -0.01117116, ..., -0.01275049,\n","        -0.01118009,  0.00134033],\n","       [-0.01330917, -0.01224558, -0.00590487, ..., -0.0094656 ,\n","        -0.02285307, -0.01990072],\n","       [-0.02089125, -0.01482844, -0.00629151, ..., -0.01262802,\n","        -0.02106232, -0.01747356]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>beta1</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.05507 0.02629 ... 0.03623</div><input id='attrs-1ce0e9fa-b66b-4754-a778-56b4511baf69' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-1ce0e9fa-b66b-4754-a778-56b4511baf69' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-48a7dfad-8399-4825-8800-0e6ae81f4ec0' class='xr-var-data-in' type='checkbox'><label for='data-48a7dfad-8399-4825-8800-0e6ae81f4ec0' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.05506617, 0.02629292, 0.03537937, ..., 0.058328  , 0.06063268,\n","        0.01260604],\n","       [0.00624328, 0.00036631, 0.02014283, ..., 0.04296559, 0.00502894,\n","        0.0270302 ],\n","       [0.02781934, 0.01572067, 0.01348607, ..., 0.03239271, 0.02024269,\n","        0.02240061],\n","       [0.02866567, 0.02972492, 0.02700153, ..., 0.02636136, 0.00762565,\n","        0.0362328 ]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>sigma</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.6614 0.6664 ... 0.6535 0.6634</div><input id='attrs-012893d8-94be-4ee1-b7a5-ffbf7e9c6a9e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-012893d8-94be-4ee1-b7a5-ffbf7e9c6a9e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-194768e9-5c23-4237-aa4f-70d27bd7d563' class='xr-var-data-in' type='checkbox'><label for='data-194768e9-5c23-4237-aa4f-70d27bd7d563' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.66142686, 0.66637419, 0.65579543, ..., 0.65449467, 0.65362803,\n","        0.65918824],\n","       [0.66204145, 0.66435729, 0.65983933, ..., 0.66842725, 0.65466736,\n","        0.64772207],\n","       [0.66758454, 0.65622678, 0.65256231, ..., 0.65964412, 0.66062044,\n","        0.66360771],\n","       [0.67526227, 0.64943534, 0.64982582, ..., 0.6628104 , 0.65351505,\n","        0.66344457]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-5c1fb72f-e8fd-4d94-a5a8-365f1ce8acf1' class='xr-section-summary-in' type='checkbox'  ><label for='section-5c1fb72f-e8fd-4d94-a5a8-365f1ce8acf1' class='xr-section-summary' >Indexes: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>chain</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-fba0727f-fbdd-44fb-b413-ad4ce8586004' class='xr-index-data-in' type='checkbox'/><label for='index-fba0727f-fbdd-44fb-b413-ad4ce8586004' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([0, 1, 2, 3], dtype=&#x27;int64&#x27;, name=&#x27;chain&#x27;))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>draw</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-831a331d-eca0-4604-a177-2eef6eb7cf51' class='xr-index-data-in' type='checkbox'/><label for='index-831a331d-eca0-4604-a177-2eef6eb7cf51' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,\n","            ...\n","            1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999],\n","           dtype=&#x27;int64&#x27;, name=&#x27;draw&#x27;, length=2000))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-cbbfd3f4-d1a4-4b73-a547-e91ae734350c' class='xr-section-summary-in' type='checkbox'  checked><label for='section-cbbfd3f4-d1a4-4b73-a547-e91ae734350c' class='xr-section-summary' >Attributes: <span>(6)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-09-17T02:55:38.498221</dd><dt><span>arviz_version :</span></dt><dd>0.14.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.0</dd><dt><span>sampling_time :</span></dt><dd>22.513349771499634</dd><dt><span>tuning_steps :</span></dt><dd>1000</dd></dl></div></li></ul></div></div><br></div>\n","                      </ul>\n","                  </div>\n","            </li>\n","            \n","            <li class = \"xr-section-item\">\n","                  <input id=\"idata_predictionsa11a407d-1d18-48c0-9737-21ae8d18bc65\" class=\"xr-section-summary-in\" type=\"checkbox\">\n","                  <label for=\"idata_predictionsa11a407d-1d18-48c0-9737-21ae8d18bc65\" class = \"xr-section-summary\">predictions</label>\n","                  <div class=\"xr-section-inline-details\"></div>\n","                  <div class=\"xr-section-details\">\n","                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n","                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n","<defs>\n","<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n","<path 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auto;\n","}\n","\n",".xr-array-wrap > label {\n","  grid-column: 1;\n","  vertical-align: top;\n","}\n","\n",".xr-preview {\n","  color: var(--xr-font-color3);\n","}\n","\n",".xr-array-preview,\n",".xr-array-data {\n","  padding: 0 5px !important;\n","  grid-column: 2;\n","}\n","\n",".xr-array-data,\n",".xr-array-in:checked ~ .xr-array-preview {\n","  display: none;\n","}\n","\n",".xr-array-in:checked ~ .xr-array-data,\n",".xr-array-preview {\n","  display: inline-block;\n","}\n","\n",".xr-dim-list {\n","  display: inline-block !important;\n","  list-style: none;\n","  padding: 0 !important;\n","  margin: 0;\n","}\n","\n",".xr-dim-list li {\n","  display: inline-block;\n","  padding: 0;\n","  margin: 0;\n","}\n","\n",".xr-dim-list:before {\n","  content: '(';\n","}\n","\n",".xr-dim-list:after {\n","  content: ')';\n","}\n","\n",".xr-dim-list li:not(:last-child):after {\n","  content: ',';\n","  padding-right: 5px;\n","}\n","\n",".xr-has-index {\n","  font-weight: bold;\n","}\n","\n",".xr-var-list,\n",".xr-var-item {\n","  display: contents;\n","}\n","\n",".xr-var-item > div,\n",".xr-var-item label,\n",".xr-var-item > .xr-var-name span {\n","  background-color: var(--xr-background-color-row-even);\n","  margin-bottom: 0;\n","}\n","\n",".xr-var-item > .xr-var-name:hover span {\n","  padding-right: 5px;\n","}\n","\n",".xr-var-list > li:nth-child(odd) > div,\n",".xr-var-list > li:nth-child(odd) > label,\n",".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n","  background-color: var(--xr-background-color-row-odd);\n","}\n","\n",".xr-var-name {\n","  grid-column: 1;\n","}\n","\n",".xr-var-dims {\n","  grid-column: 2;\n","}\n","\n",".xr-var-dtype {\n","  grid-column: 3;\n","  text-align: right;\n","  color: var(--xr-font-color2);\n","}\n","\n",".xr-var-preview {\n","  grid-column: 4;\n","}\n","\n",".xr-index-preview {\n","  grid-column: 2 / 5;\n","  color: var(--xr-font-color2);\n","}\n","\n",".xr-var-name,\n",".xr-var-dims,\n",".xr-var-dtype,\n",".xr-preview,\n",".xr-attrs dt {\n","  white-space: nowrap;\n","  overflow: hidden;\n","  text-overflow: ellipsis;\n","  padding-right: 10px;\n","}\n","\n",".xr-var-name:hover,\n",".xr-var-dims:hover,\n",".xr-var-dtype:hover,\n",".xr-attrs dt:hover {\n","  overflow: visible;\n","  width: auto;\n","  z-index: 1;\n","}\n","\n",".xr-var-attrs,\n",".xr-var-data,\n",".xr-index-data {\n","  display: none;\n","  background-color: var(--xr-background-color) !important;\n","  padding-bottom: 5px !important;\n","}\n","\n",".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",".xr-var-data-in:checked ~ .xr-var-data,\n",".xr-index-data-in:checked ~ .xr-index-data {\n","  display: block;\n","}\n","\n",".xr-var-data > table {\n","  float: right;\n","}\n","\n",".xr-var-name span,\n",".xr-var-data,\n",".xr-index-name div,\n",".xr-index-data,\n",".xr-attrs {\n","  padding-left: 25px !important;\n","}\n","\n",".xr-attrs,\n",".xr-var-attrs,\n",".xr-var-data,\n",".xr-index-data {\n","  grid-column: 1 / -1;\n","}\n","\n","dl.xr-attrs {\n","  padding: 0;\n","  margin: 0;\n","  display: grid;\n","  grid-template-columns: 125px auto;\n","}\n","\n",".xr-attrs dt,\n",".xr-attrs dd {\n","  padding: 0;\n","  margin: 0;\n","  float: left;\n","  padding-right: 10px;\n","  width: auto;\n","}\n","\n",".xr-attrs dt {\n","  font-weight: normal;\n","  grid-column: 1;\n","}\n","\n",".xr-attrs dt:hover span {\n","  display: inline-block;\n","  background: var(--xr-background-color);\n","  padding-right: 10px;\n","}\n","\n",".xr-attrs dd {\n","  grid-column: 2;\n","  white-space: pre-wrap;\n","  word-break: break-all;\n","}\n","\n",".xr-icon-database,\n",".xr-icon-file-text2,\n",".xr-no-icon {\n","  display: inline-block;\n","  vertical-align: middle;\n","  width: 1em;\n","  height: 1.5em !important;\n","  stroke-width: 0;\n","  stroke: currentColor;\n","  fill: currentColor;\n","}\n","</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n","Dimensions:  (chain: 4, draw: 2000, y_dim_2: 6905)\n","Coordinates:\n","  * chain    (chain) int64 0 1 2 3\n","  * draw     (draw) int64 0 1 2 3 4 5 6 7 ... 1993 1994 1995 1996 1997 1998 1999\n","  * y_dim_2  (y_dim_2) int64 0 1 2 3 4 5 6 ... 6899 6900 6901 6902 6903 6904\n","Data variables:\n","    y        (chain, draw, y_dim_2) float64 0.4933 -0.8639 ... -0.2184 -0.7816\n","Attributes:\n","    created_at:                 2023-09-17T02:55:48.233199\n","    arviz_version:              0.14.0\n","    inference_library:          pymc\n","    inference_library_version:  5.6.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-9a978eec-e8d9-446c-acb5-d6eb281c948e' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-9a978eec-e8d9-446c-acb5-d6eb281c948e' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 4</li><li><span class='xr-has-index'>draw</span>: 2000</li><li><span class='xr-has-index'>y_dim_2</span>: 6905</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-2cf94028-4dab-405e-9a35-cca06895fd63' class='xr-section-summary-in' type='checkbox'  checked><label for='section-2cf94028-4dab-405e-9a35-cca06895fd63' class='xr-section-summary' >Coordinates: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3</div><input id='attrs-516436fb-68a1-4160-af23-7997f22588fd' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-516436fb-68a1-4160-af23-7997f22588fd' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-b5df8f1a-d8d1-4a2a-9bad-a3bd83fe39d8' class='xr-var-data-in' type='checkbox'><label for='data-b5df8f1a-d8d1-4a2a-9bad-a3bd83fe39d8' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 2, 3])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 1996 1997 1998 1999</div><input id='attrs-37d39a0e-ccd3-494f-9a75-7d0cb9e0bda7' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-37d39a0e-ccd3-494f-9a75-7d0cb9e0bda7' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-90510626-b975-4361-ad79-f251675b0b2f' class='xr-var-data-in' type='checkbox'><label for='data-90510626-b975-4361-ad79-f251675b0b2f' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 1997, 1998, 1999])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>y_dim_2</span></div><div class='xr-var-dims'>(y_dim_2)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 6901 6902 6903 6904</div><input id='attrs-e2084f2e-a075-4581-ba8a-1be7ad60b55a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-e2084f2e-a075-4581-ba8a-1be7ad60b55a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-021e1970-37f1-46fb-8d39-4f02cf4f3122' class='xr-var-data-in' type='checkbox'><label for='data-021e1970-37f1-46fb-8d39-4f02cf4f3122' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 6902, 6903, 6904])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-42ef5851-8971-44b9-995a-b409b7f26b82' class='xr-section-summary-in' type='checkbox'  checked><label for='section-42ef5851-8971-44b9-995a-b409b7f26b82' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>y</span></div><div class='xr-var-dims'>(chain, draw, y_dim_2)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.4933 -0.8639 ... -0.2184 -0.7816</div><input id='attrs-36023e65-1ca8-433e-942b-e659c25df78e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-36023e65-1ca8-433e-942b-e659c25df78e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-be0dc32e-ba05-496e-ba10-4ea0fdc37df1' class='xr-var-data-in' type='checkbox'><label for='data-be0dc32e-ba05-496e-ba10-4ea0fdc37df1' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[ 0.49331084, -0.86391326, -0.31739099, ...,  0.86979553,\n","         -0.54127835, -0.23632393],\n","        [ 0.7959879 , -0.09477495,  1.3213892 , ...,  0.14666571,\n","         -1.74526338, -0.22991846],\n","        [-0.63339014, -0.33216732,  0.90684232, ..., -0.11258073,\n","          0.62328326, -0.10866267],\n","        ...,\n","        [-0.4798836 ,  0.9071782 , -0.09293086, ...,  0.78497266,\n","         -0.62193731,  0.92437843],\n","        [-0.28417699, -0.56958408, -0.29978095, ...,  0.32526807,\n","         -0.26443132,  0.45440459],\n","        [-0.85605588, -0.31384798, -0.41135587, ...,  1.17652257,\n","         -0.06296293,  0.15558073]],\n","\n","       [[-1.23009862, -0.72531454,  0.21738673, ..., -0.48742632,\n","         -0.63063583,  0.69063735],\n","        [-0.02624998, -0.35641768, -0.56331859, ...,  0.11593782,\n","         -0.8623884 , -0.09569105],\n","        [-0.30554834,  0.06829514, -0.36177883, ..., -0.75153941,\n","          1.29792427, -0.19780852],\n","...\n","        [-0.17805979, -0.86433986,  0.45397626, ..., -0.82634061,\n","         -0.04431099,  0.15886444],\n","        [-1.77712692,  0.28741151,  0.15315464, ...,  0.63030577,\n","          0.95780345,  0.50811723],\n","        [-0.67539265,  1.21871331,  0.34818093, ...,  0.47706363,\n","          0.80911636, -0.6918712 ]],\n","\n","       [[-0.66153025,  0.28947795,  0.12583548, ...,  0.86129545,\n","         -1.28909778,  0.21297488],\n","        [ 0.27359942,  0.21056239, -0.76605727, ...,  0.03461055,\n","         -1.28375747,  0.29548159],\n","        [-0.20804753,  0.11278566, -1.00679803, ..., -0.20187723,\n","          1.37905085,  0.47808417],\n","        ...,\n","        [ 0.47273881, -0.17078875, -0.46119668, ..., -0.30372419,\n","          0.50147375, -0.1543189 ],\n","        [ 0.4213556 , -0.14662485, -0.25644111, ...,  0.71277173,\n","          0.58321929, -0.08695745],\n","        [ 0.29304571, -0.26267844,  0.79570875, ...,  0.06554506,\n","         -0.21844279, -0.78157348]]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-c2f6fc3e-4eaf-4414-82e5-cd8053ce315e' class='xr-section-summary-in' type='checkbox'  ><label for='section-c2f6fc3e-4eaf-4414-82e5-cd8053ce315e' class='xr-section-summary' >Indexes: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>chain</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-8c6c8099-9778-47f9-9983-2483b6bf1b7c' class='xr-index-data-in' type='checkbox'/><label for='index-8c6c8099-9778-47f9-9983-2483b6bf1b7c' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([0, 1, 2, 3], dtype=&#x27;int64&#x27;, name=&#x27;chain&#x27;))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>draw</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-db00d482-99d4-4268-83cf-424e00dfd314' class='xr-index-data-in' type='checkbox'/><label for='index-db00d482-99d4-4268-83cf-424e00dfd314' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,\n","            ...\n","            1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999],\n","           dtype=&#x27;int64&#x27;, name=&#x27;draw&#x27;, length=2000))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>y_dim_2</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-b7b139e7-0ead-415b-bbb4-ff5e78fa8e36' class='xr-index-data-in' type='checkbox'/><label for='index-b7b139e7-0ead-415b-bbb4-ff5e78fa8e36' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,\n","            ...\n","            6895, 6896, 6897, 6898, 6899, 6900, 6901, 6902, 6903, 6904],\n","           dtype=&#x27;int64&#x27;, name=&#x27;y_dim_2&#x27;, length=6905))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-12c382bc-b8dc-41a2-a8d4-5c0039f975cd' class='xr-section-summary-in' type='checkbox'  checked><label for='section-12c382bc-b8dc-41a2-a8d4-5c0039f975cd' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-09-17T02:55:48.233199</dd><dt><span>arviz_version :</span></dt><dd>0.14.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.0</dd></dl></div></li></ul></div></div><br></div>\n","                      </ul>\n","                  </div>\n","            </li>\n","            \n","       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auto;\n","}\n","\n",".xr-attrs dt {\n","  font-weight: normal;\n","  grid-column: 1;\n","}\n","\n",".xr-attrs dt:hover span {\n","  display: inline-block;\n","  background: var(--xr-background-color);\n","  padding-right: 10px;\n","}\n","\n",".xr-attrs dd {\n","  grid-column: 2;\n","  white-space: pre-wrap;\n","  word-break: break-all;\n","}\n","\n",".xr-icon-database,\n",".xr-icon-file-text2,\n",".xr-no-icon {\n","  display: inline-block;\n","  vertical-align: middle;\n","  width: 1em;\n","  height: 1.5em !important;\n","  stroke-width: 0;\n","  stroke: currentColor;\n","  fill: currentColor;\n","}\n","</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n","Dimensions:                (chain: 4, draw: 2000)\n","Coordinates:\n","  * chain                  (chain) int64 0 1 2 3\n","  * draw                   (draw) int64 0 1 2 3 4 5 ... 1995 1996 1997 1998 1999\n","Data variables: (12/17)\n","    reached_max_treedepth  (chain, draw) bool False False False ... False False\n","    diverging              (chain, draw) bool False False False ... False False\n","    energy_error           (chain, draw) float64 0.3343 -0.1113 ... 1.124 -1.077\n","    step_size              (chain, draw) float64 0.568 0.568 ... 0.7599 0.7599\n","    process_time_diff      (chain, draw) float64 0.001591 0.003106 ... 0.002622\n","    step_size_bar          (chain, draw) float64 0.6257 0.6257 ... 0.6324 0.6324\n","    ...                     ...\n","    n_steps                (chain, draw) float64 3.0 7.0 7.0 7.0 ... 3.0 7.0 7.0\n","    perf_counter_start     (chain, draw) float64 1.022e+06 ... 1.022e+06\n","    lp                     (chain, draw) float64 -6.942e+03 ... -6.94e+03\n","    largest_eigval         (chain, draw) float64 nan nan nan nan ... nan nan nan\n","    tree_depth             (chain, draw) int64 2 3 3 3 2 3 3 2 ... 3 3 2 3 2 3 3\n","    perf_counter_diff      (chain, draw) float64 0.00159 0.003106 ... 0.002621\n","Attributes:\n","    created_at:                 2023-09-17T02:55:38.527278\n","    arviz_version:              0.14.0\n","    inference_library:          pymc\n","    inference_library_version:  5.6.0\n","    sampling_time:              22.513349771499634\n","    tuning_steps:               1000</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-e6f15f11-1200-49b3-b0d2-ef77dc8a45d4' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-e6f15f11-1200-49b3-b0d2-ef77dc8a45d4' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 4</li><li><span class='xr-has-index'>draw</span>: 2000</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-1f038a50-acf1-4311-8b0e-8760926b8c01' class='xr-section-summary-in' type='checkbox'  checked><label for='section-1f038a50-acf1-4311-8b0e-8760926b8c01' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3</div><input id='attrs-eb7c622c-a1a1-42b4-98ab-7cd0ccda28c2' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-eb7c622c-a1a1-42b4-98ab-7cd0ccda28c2' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-46bb0573-68af-44f9-a885-236e2efb8e69' class='xr-var-data-in' type='checkbox'><label for='data-46bb0573-68af-44f9-a885-236e2efb8e69' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 2, 3])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 1996 1997 1998 1999</div><input id='attrs-3cfe898f-f126-4f28-899e-6652c0a305ba' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-3cfe898f-f126-4f28-899e-6652c0a305ba' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-88dd7e0e-638c-4e58-8d1e-58f5601aeb55' class='xr-var-data-in' type='checkbox'><label for='data-88dd7e0e-638c-4e58-8d1e-58f5601aeb55' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 1997, 1998, 1999])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-beddc0af-612a-4380-94c1-eb95d1e2a52c' class='xr-section-summary-in' type='checkbox'  ><label for='section-beddc0af-612a-4380-94c1-eb95d1e2a52c' class='xr-section-summary' >Data variables: <span>(17)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>reached_max_treedepth</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>bool</div><div class='xr-var-preview xr-preview'>False False False ... False False</div><input id='attrs-21cedbe9-fe61-4416-bf42-818431a5db5a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-21cedbe9-fe61-4416-bf42-818431a5db5a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-ce421521-48b1-4e19-a975-3e66fdc24033' class='xr-var-data-in' type='checkbox'><label for='data-ce421521-48b1-4e19-a975-3e66fdc24033' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[False, False, False, ..., False, False, False],\n","       [False, False, False, ..., False, False, False],\n","       [False, False, False, ..., False, False, False],\n","       [False, False, False, ..., False, False, False]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>diverging</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>bool</div><div class='xr-var-preview xr-preview'>False False False ... False False</div><input id='attrs-962aa328-dde7-40d1-b5d3-6661d81ff508' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-962aa328-dde7-40d1-b5d3-6661d81ff508' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-83ec5b26-19b9-45e1-b42e-72d7a370ac29' class='xr-var-data-in' type='checkbox'><label for='data-83ec5b26-19b9-45e1-b42e-72d7a370ac29' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[False, False, False, ..., False, False, False],\n","       [False, False, False, ..., False, False, False],\n","       [False, False, False, ..., False, False, False],\n","       [False, False, False, ..., False, False, False]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>energy_error</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.3343 -0.1113 ... 1.124 -1.077</div><input id='attrs-b44ddd89-1100-4429-a5e3-62ca5c3dfe8f' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b44ddd89-1100-4429-a5e3-62ca5c3dfe8f' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-985c8d99-4b6a-4add-9d9f-7001ed01283d' class='xr-var-data-in' type='checkbox'><label for='data-985c8d99-4b6a-4add-9d9f-7001ed01283d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[ 0.3343132 , -0.11125342, -0.06702623, ...,  0.161389  ,\n","         0.01203837, -0.10568408],\n","       [ 0.00508962,  0.08159425, -0.13192237, ...,  0.30791133,\n","         0.08904438,  0.25308439],\n","       [-0.34505076,  0.07617857, -0.0299948 , ...,  0.01321436,\n","         0.34276216, -0.24305429],\n","       [ 0.40111387, -0.21744964,  0.10848535, ..., -0.01679606,\n","         1.12363327, -1.07749648]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>step_size</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.568 0.568 0.568 ... 0.7599 0.7599</div><input id='attrs-096eb866-b74a-4d3e-a037-4dcf0875843f' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-096eb866-b74a-4d3e-a037-4dcf0875843f' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-e3ccf4c9-e551-495e-843b-eb034b412b98' class='xr-var-data-in' type='checkbox'><label for='data-e3ccf4c9-e551-495e-843b-eb034b412b98' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.56795723, 0.56795723, 0.56795723, ..., 0.56795723, 0.56795723,\n","        0.56795723],\n","       [0.51509001, 0.51509001, 0.51509001, ..., 0.51509001, 0.51509001,\n","        0.51509001],\n","       [0.56437868, 0.56437868, 0.56437868, ..., 0.56437868, 0.56437868,\n","        0.56437868],\n","       [0.75985803, 0.75985803, 0.75985803, ..., 0.75985803, 0.75985803,\n","        0.75985803]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>process_time_diff</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.001591 0.003106 ... 0.002622</div><input id='attrs-1226b1fd-0d5a-44fd-92b7-cb19f98bc1b7' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-1226b1fd-0d5a-44fd-92b7-cb19f98bc1b7' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-495f617c-9932-4188-bdb4-1515d8b11a08' class='xr-var-data-in' type='checkbox'><label for='data-495f617c-9932-4188-bdb4-1515d8b11a08' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.00159075, 0.00310641, 0.0034873 , ..., 0.00107263, 0.00159045,\n","        0.00228249],\n","       [0.00197023, 0.00106926, 0.00108999, ..., 0.00242125, 0.00274279,\n","        0.00149447],\n","       [0.00197165, 0.00210003, 0.00247894, ..., 0.00093349, 0.00096316,\n","        0.00098576],\n","       [0.00102832, 0.00195093, 0.00298834, ..., 0.00137613, 0.00286004,\n","        0.00262164]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>step_size_bar</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.6257 0.6257 ... 0.6324 0.6324</div><input id='attrs-f9cf1114-eadf-47d2-a29c-78184a8ddf0c' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-f9cf1114-eadf-47d2-a29c-78184a8ddf0c' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-1276b05a-c9da-4ccc-8e7b-4714192343dc' class='xr-var-data-in' type='checkbox'><label for='data-1276b05a-c9da-4ccc-8e7b-4714192343dc' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.6256917 , 0.6256917 , 0.6256917 , ..., 0.6256917 , 0.6256917 ,\n","        0.6256917 ],\n","       [0.55335105, 0.55335105, 0.55335105, ..., 0.55335105, 0.55335105,\n","        0.55335105],\n","       [0.59919843, 0.59919843, 0.59919843, ..., 0.59919843, 0.59919843,\n","        0.59919843],\n","       [0.63240817, 0.63240817, 0.63240817, ..., 0.63240817, 0.63240817,\n","        0.63240817]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>index_in_trajectory</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>-2 2 -5 1 -2 2 5 ... 5 -4 3 3 2 4 2</div><input id='attrs-c4104bfb-4d82-499d-8a00-b9c8bdc94393' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-c4104bfb-4d82-499d-8a00-b9c8bdc94393' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-45c833df-b19c-4d4f-8834-bd29c45cde0d' class='xr-var-data-in' type='checkbox'><label for='data-45c833df-b19c-4d4f-8834-bd29c45cde0d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[-2,  2, -5, ..., -2, -1, -2],\n","       [-3,  1, -1, ...,  2,  7,  2],\n","       [ 3, -4, -3, ...,  2,  1, -1],\n","       [ 2, -4,  1, ...,  2,  4,  2]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>smallest_eigval</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>nan nan nan nan ... nan nan nan nan</div><input id='attrs-a43c15bd-9abd-40ca-a186-39da2ff79213' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-a43c15bd-9abd-40ca-a186-39da2ff79213' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-afef93eb-18cc-43bd-ab54-c140bf996df5' class='xr-var-data-in' type='checkbox'><label for='data-afef93eb-18cc-43bd-ab54-c140bf996df5' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[nan, nan, nan, ..., nan, nan, nan],\n","       [nan, nan, nan, ..., nan, nan, nan],\n","       [nan, nan, nan, ..., nan, nan, nan],\n","       [nan, nan, nan, ..., nan, nan, nan]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>max_energy_error</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.3343 -0.3357 ... 1.124 1.173</div><input id='attrs-1dff7acc-27a3-4454-8f5d-7acfb0ee07f3' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-1dff7acc-27a3-4454-8f5d-7acfb0ee07f3' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d779d660-b4f6-4e45-ba3c-40c6d124de3c' class='xr-var-data-in' type='checkbox'><label for='data-d779d660-b4f6-4e45-ba3c-40c6d124de3c' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[ 0.3343132 , -0.33567335, -0.25850326, ...,  0.34372417,\n","        -0.19346789, -0.19161568],\n","       [ 0.22139547,  0.08159425,  0.19325631, ...,  0.35965461,\n","        -0.33127988, -0.29665111],\n","       [-0.34505076,  0.11551835,  0.40404355, ...,  0.24304313,\n","         0.71455189, -0.28491821],\n","       [ 0.40111387, -0.3240351 ,  0.13064112, ..., -0.01685061,\n","         1.12363327,  1.17327504]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>acceptance_rate</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.8262 1.0 0.9547 ... 0.5457 0.7304</div><input id='attrs-aaf8df45-3a44-4846-ab6a-e13e6c614e87' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-aaf8df45-3a44-4846-ab6a-e13e6c614e87' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-fb83ed62-e031-46d9-9025-08e1751e9731' class='xr-var-data-in' type='checkbox'><label for='data-fb83ed62-e031-46d9-9025-08e1751e9731' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.82620166, 1.        , 0.95474528, ..., 0.82603466, 0.99601127,\n","        0.96776049],\n","       [0.88407417, 0.9479077 , 0.91299205, ..., 0.84881884, 0.94844006,\n","        0.92546745],\n","       [0.99829917, 0.96379096, 0.85579756, ..., 0.8903508 , 0.60253162,\n","        0.97690392],\n","       [0.70204236, 1.        , 0.96357745, ..., 0.9952362 , 0.54569166,\n","        0.73040654]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>energy</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>6.942e+03 6.942e+03 ... 6.946e+03</div><input id='attrs-743a7943-8caa-43c0-a3e7-d595fe5f0e72' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-743a7943-8caa-43c0-a3e7-d595fe5f0e72' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-1dad26fe-82e3-4e56-9160-ac83c0c0c0e4' class='xr-var-data-in' type='checkbox'><label for='data-1dad26fe-82e3-4e56-9160-ac83c0c0c0e4' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[6942.19842178, 6942.37682391, 6943.41319108, ..., 6943.16246061,\n","        6943.08383076, 6945.23077656],\n","       [6941.91698339, 6941.92662328, 6944.84420471, ..., 6942.7745564 ,\n","        6945.03034034, 6944.73298349],\n","       [6946.94794125, 6941.31765923, 6943.05230571, ..., 6942.10162453,\n","        6942.32766037, 6941.7290516 ],\n","       [6944.12793657, 6943.51603582, 6943.0872786 , ..., 6940.25544362,\n","        6944.88602426, 6946.04037273]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>n_steps</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>3.0 7.0 7.0 7.0 ... 7.0 3.0 7.0 7.0</div><input id='attrs-2b7d3fc3-ff2b-4511-aec4-801d486bc6b8' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-2b7d3fc3-ff2b-4511-aec4-801d486bc6b8' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-21224c70-e3e2-4da8-9d6b-395db5d8ae1d' class='xr-var-data-in' type='checkbox'><label for='data-21224c70-e3e2-4da8-9d6b-395db5d8ae1d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[3., 7., 7., ..., 3., 3., 7.],\n","       [7., 3., 3., ..., 7., 7., 3.],\n","       [7., 7., 7., ..., 3., 3., 3.],\n","       [3., 7., 7., ..., 3., 7., 7.]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>perf_counter_start</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.022e+06 1.022e+06 ... 1.022e+06</div><input id='attrs-b5eb0b7f-60c0-4130-a50c-59d8c1510ebf' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b5eb0b7f-60c0-4130-a50c-59d8c1510ebf' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-97696d96-6e3e-4253-8a3f-77316ee865e2' class='xr-var-data-in' type='checkbox'><label for='data-97696d96-6e3e-4253-8a3f-77316ee865e2' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[1022245.22652437, 1022245.22840382, 1022245.23177772, ...,\n","        1022258.04745679, 1022258.10049461, 1022258.10232635],\n","       [1022244.62910002, 1022244.63129084, 1022244.63255106, ...,\n","        1022257.92545204, 1022257.92807887, 1022257.93103999],\n","       [1022246.12969317, 1022246.13187209, 1022246.13420155, ...,\n","        1022258.52003832, 1022258.52117392, 1022258.52231674],\n","       [1022245.61386747, 1022245.61510987, 1022245.61837651, ...,\n","        1022258.54877052, 1022258.55042916, 1022258.5535293 ]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>lp</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-6.942e+03 -6.941e+03 ... -6.94e+03</div><input id='attrs-7ee10b85-e516-4fc1-921f-f7f9b44f90bf' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-7ee10b85-e516-4fc1-921f-f7f9b44f90bf' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-1682786b-7c5a-4229-bb73-c35b8f4c61cc' class='xr-var-data-in' type='checkbox'><label for='data-1682786b-7c5a-4229-bb73-c35b8f4c61cc' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[-6941.89464603, -6941.32361339, -6941.2917676 , ...,\n","        -6942.47602069, -6942.95240697, -6940.69766493],\n","       [-6941.22753747, -6941.77197871, -6940.17401924, ...,\n","        -6942.04866781, -6942.24436404, -6944.52954784],\n","       [-6940.82364061, -6940.78023027, -6941.48201772, ...,\n","        -6940.45219392, -6941.43087141, -6940.83913425],\n","       [-6943.68937512, -6942.0311428 , -6942.31709702, ...,\n","        -6940.12981528, -6944.05801318, -6940.31218699]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>largest_eigval</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>nan nan nan nan ... nan nan nan nan</div><input id='attrs-97f9f7c2-d0f1-442c-a14c-326c9bde350c' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-97f9f7c2-d0f1-442c-a14c-326c9bde350c' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-5cfdef9a-faa1-441e-b1f2-cfe426ba74cb' class='xr-var-data-in' type='checkbox'><label for='data-5cfdef9a-faa1-441e-b1f2-cfe426ba74cb' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[nan, nan, nan, ..., nan, nan, nan],\n","       [nan, nan, nan, ..., nan, nan, nan],\n","       [nan, nan, nan, ..., nan, nan, nan],\n","       [nan, nan, nan, ..., nan, nan, nan]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>tree_depth</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>2 3 3 3 2 3 3 2 ... 3 3 3 2 3 2 3 3</div><input id='attrs-0557f1b6-06a6-4217-b984-2c592a79e150' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-0557f1b6-06a6-4217-b984-2c592a79e150' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-b1c5dfaf-13be-4aa4-b479-72c14d248764' class='xr-var-data-in' type='checkbox'><label for='data-b1c5dfaf-13be-4aa4-b479-72c14d248764' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[2, 3, 3, ..., 2, 2, 3],\n","       [3, 2, 2, ..., 3, 3, 2],\n","       [3, 3, 3, ..., 2, 2, 2],\n","       [2, 3, 3, ..., 2, 3, 3]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>perf_counter_diff</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.00159 0.003106 ... 0.002621</div><input id='attrs-f95f4e18-0ae0-44a2-9d46-f3b64d3e2462' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-f95f4e18-0ae0-44a2-9d46-f3b64d3e2462' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-0b2b3a0f-83af-4690-a82d-401cacb44cc2' class='xr-var-data-in' type='checkbox'><label for='data-0b2b3a0f-83af-4690-a82d-401cacb44cc2' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.00159023, 0.0031058 , 0.06949511, ..., 0.00107172, 0.00159118,\n","        0.0022823 ],\n","       [0.00196995, 0.00106847, 0.0010888 , ..., 0.00242073, 0.00274218,\n","        0.00149386],\n","       [0.0019711 , 0.00209938, 0.06746579, ..., 0.00093282, 0.00096296,\n","        0.00098509],\n","       [0.00102767, 0.00195087, 0.00298792, ..., 0.00137578, 0.00285995,\n","        0.00262139]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-882fcd24-7407-4d82-b24f-9a8bdd2374be' class='xr-section-summary-in' type='checkbox'  ><label for='section-882fcd24-7407-4d82-b24f-9a8bdd2374be' class='xr-section-summary' >Indexes: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>chain</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-74ea5f02-b75b-4147-9021-2e871aff6046' class='xr-index-data-in' type='checkbox'/><label for='index-74ea5f02-b75b-4147-9021-2e871aff6046' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([0, 1, 2, 3], dtype=&#x27;int64&#x27;, name=&#x27;chain&#x27;))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>draw</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-67f308bd-8356-4603-83ca-16a44276d4fe' class='xr-index-data-in' type='checkbox'/><label for='index-67f308bd-8356-4603-83ca-16a44276d4fe' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,\n","            ...\n","            1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999],\n","           dtype=&#x27;int64&#x27;, name=&#x27;draw&#x27;, length=2000))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-70873125-8104-4d0d-9d40-3be3d3b783ce' class='xr-section-summary-in' type='checkbox'  checked><label for='section-70873125-8104-4d0d-9d40-3be3d3b783ce' class='xr-section-summary' >Attributes: <span>(6)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-09-17T02:55:38.527278</dd><dt><span>arviz_version :</span></dt><dd>0.14.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.0</dd><dt><span>sampling_time :</span></dt><dd>22.513349771499634</dd><dt><span>tuning_steps :</span></dt><dd>1000</dd></dl></div></li></ul></div></div><br></div>\n","                      </ul>\n","                  </div>\n","            </li>\n","            \n","            <li class = \"xr-section-item\">\n","                  <input id=\"idata_observed_datafe0e25f5-ba74-4a9e-9296-325cd26debbf\" class=\"xr-section-summary-in\" type=\"checkbox\">\n","                  <label for=\"idata_observed_datafe0e25f5-ba74-4a9e-9296-325cd26debbf\" class = \"xr-section-summary\">observed_data</label>\n","                  <div class=\"xr-section-inline-details\"></div>\n","                  <div class=\"xr-section-details\">\n","                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n","                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n","<defs>\n","<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n","<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n","<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n","<path d=\"M16 26c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n","</symbol>\n","<symbol id=\"icon-file-text2\" viewBox=\"0 0 32 32\">\n","<path d=\"M28.681 7.159c-0.694-0.947-1.662-2.053-2.724-3.116s-2.169-2.030-3.116-2.724c-1.612-1.182-2.393-1.319-2.841-1.319h-15.5c-1.378 0-2.5 1.121-2.5 2.5v27c0 1.378 1.122 2.5 2.5 2.5h23c1.378 0 2.5-1.122 2.5-2.5v-19.5c0-0.448-0.137-1.23-1.319-2.841zM24.543 5.457c0.959 0.959 1.712 1.825 2.268 2.543h-4.811v-4.811c0.718 0.556 1.584 1.309 2.543 2.268zM28 29.5c0 0.271-0.229 0.5-0.5 0.5h-23c-0.271 0-0.5-0.229-0.5-0.5v-27c0-0.271 0.229-0.5 0.5-0.5 0 0 15.499-0 15.5 0v7c0 0.552 0.448 1 1 1h7v19.5z\"></path>\n","<path d=\"M23 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#eeeeee);\n","}\n","\n","html[theme=dark],\n","body[data-theme=dark],\n","body.vscode-dark {\n","  --xr-font-color0: rgba(255, 255, 255, 1);\n","  --xr-font-color2: rgba(255, 255, 255, 0.54);\n","  --xr-font-color3: rgba(255, 255, 255, 0.38);\n","  --xr-border-color: #1F1F1F;\n","  --xr-disabled-color: #515151;\n","  --xr-background-color: #111111;\n","  --xr-background-color-row-even: #111111;\n","  --xr-background-color-row-odd: #313131;\n","}\n","\n",".xr-wrap {\n","  display: block !important;\n","  min-width: 300px;\n","  max-width: 700px;\n","}\n","\n",".xr-text-repr-fallback {\n","  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n","  display: none;\n","}\n","\n",".xr-header {\n","  padding-top: 6px;\n","  padding-bottom: 6px;\n","  margin-bottom: 4px;\n","  border-bottom: solid 1px var(--xr-border-color);\n","}\n","\n",".xr-header > div,\n",".xr-header > ul {\n","  display: inline;\n","  margin-top: 0;\n","  margin-bottom: 0;\n","}\n","\n",".xr-obj-type,\n",".xr-array-name {\n","  margin-left: 2px;\n","  margin-right: 10px;\n","}\n","\n",".xr-obj-type {\n","  color: var(--xr-font-color2);\n","}\n","\n",".xr-sections {\n","  padding-left: 0 !important;\n","  display: grid;\n","  grid-template-columns: 150px auto auto 1fr 20px 20px;\n","}\n","\n",".xr-section-item {\n","  display: contents;\n","}\n","\n",".xr-section-item input {\n","  display: none;\n","}\n","\n",".xr-section-item input + label {\n","  color: var(--xr-disabled-color);\n","}\n","\n",".xr-section-item input:enabled + label {\n","  cursor: pointer;\n","  color: var(--xr-font-color2);\n","}\n","\n",".xr-section-item input:enabled + label:hover {\n","  color: var(--xr-font-color0);\n","}\n","\n",".xr-section-summary {\n","  grid-column: 1;\n","  color: var(--xr-font-color2);\n","  font-weight: 500;\n","}\n","\n",".xr-section-summary > span {\n","  display: inline-block;\n","  padding-left: 0.5em;\n","}\n","\n",".xr-section-summary-in:disabled + label {\n","  color: var(--xr-font-color2);\n","}\n","\n",".xr-section-summary-in + label:before {\n","  display: inline-block;\n","  content: '►';\n","  font-size: 11px;\n","  width: 15px;\n","  text-align: center;\n","}\n","\n",".xr-section-summary-in:disabled + label:before {\n","  color: var(--xr-disabled-color);\n","}\n","\n",".xr-section-summary-in:checked + label:before {\n","  content: '▼';\n","}\n","\n",".xr-section-summary-in:checked + label > span {\n","  display: none;\n","}\n","\n",".xr-section-summary,\n",".xr-section-inline-details {\n","  padding-top: 4px;\n","  padding-bottom: 4px;\n","}\n","\n",".xr-section-inline-details {\n","  grid-column: 2 / -1;\n","}\n","\n",".xr-section-details {\n","  display: none;\n","  grid-column: 1 / -1;\n","  margin-bottom: 5px;\n","}\n","\n",".xr-section-summary-in:checked ~ .xr-section-details {\n","  display: contents;\n","}\n","\n",".xr-array-wrap {\n","  grid-column: 1 / -1;\n","  display: grid;\n","  grid-template-columns: 20px auto;\n","}\n","\n",".xr-array-wrap > label {\n","  grid-column: 1;\n","  vertical-align: top;\n","}\n","\n",".xr-preview {\n","  color: var(--xr-font-color3);\n","}\n","\n",".xr-array-preview,\n",".xr-array-data {\n","  padding: 0 5px !important;\n","  grid-column: 2;\n","}\n","\n",".xr-array-data,\n",".xr-array-in:checked ~ .xr-array-preview {\n","  display: none;\n","}\n","\n",".xr-array-in:checked ~ .xr-array-data,\n",".xr-array-preview {\n","  display: inline-block;\n","}\n","\n",".xr-dim-list {\n","  display: inline-block !important;\n","  list-style: none;\n","  padding: 0 !important;\n","  margin: 0;\n","}\n","\n",".xr-dim-list li {\n","  display: inline-block;\n","  padding: 0;\n","  margin: 0;\n","}\n","\n",".xr-dim-list:before {\n","  content: '(';\n","}\n","\n",".xr-dim-list:after {\n","  content: ')';\n","}\n","\n",".xr-dim-list li:not(:last-child):after {\n","  content: ',';\n","  padding-right: 5px;\n","}\n","\n",".xr-has-index {\n","  font-weight: bold;\n","}\n","\n",".xr-var-list,\n",".xr-var-item {\n","  display: contents;\n","}\n","\n",".xr-var-item > div,\n",".xr-var-item label,\n",".xr-var-item > .xr-var-name span {\n","  background-color: var(--xr-background-color-row-even);\n","  margin-bottom: 0;\n","}\n","\n",".xr-var-item > .xr-var-name:hover span {\n","  padding-right: 5px;\n","}\n","\n",".xr-var-list > li:nth-child(odd) > div,\n",".xr-var-list > li:nth-child(odd) > label,\n",".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n","  background-color: var(--xr-background-color-row-odd);\n","}\n","\n",".xr-var-name {\n","  grid-column: 1;\n","}\n","\n",".xr-var-dims {\n","  grid-column: 2;\n","}\n","\n",".xr-var-dtype {\n","  grid-column: 3;\n","  text-align: right;\n","  color: var(--xr-font-color2);\n","}\n","\n",".xr-var-preview {\n","  grid-column: 4;\n","}\n","\n",".xr-index-preview {\n","  grid-column: 2 / 5;\n","  color: var(--xr-font-color2);\n","}\n","\n",".xr-var-name,\n",".xr-var-dims,\n",".xr-var-dtype,\n",".xr-preview,\n",".xr-attrs dt {\n","  white-space: nowrap;\n","  overflow: hidden;\n","  text-overflow: ellipsis;\n","  padding-right: 10px;\n","}\n","\n",".xr-var-name:hover,\n",".xr-var-dims:hover,\n",".xr-var-dtype:hover,\n",".xr-attrs dt:hover {\n","  overflow: visible;\n","  width: auto;\n","  z-index: 1;\n","}\n","\n",".xr-var-attrs,\n",".xr-var-data,\n",".xr-index-data {\n","  display: none;\n","  background-color: var(--xr-background-color) !important;\n","  padding-bottom: 5px !important;\n","}\n","\n",".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",".xr-var-data-in:checked ~ .xr-var-data,\n",".xr-index-data-in:checked ~ .xr-index-data {\n","  display: block;\n","}\n","\n",".xr-var-data > table {\n","  float: right;\n","}\n","\n",".xr-var-name span,\n",".xr-var-data,\n",".xr-index-name div,\n",".xr-index-data,\n",".xr-attrs {\n","  padding-left: 25px !important;\n","}\n","\n",".xr-attrs,\n",".xr-var-attrs,\n",".xr-var-data,\n",".xr-index-data {\n","  grid-column: 1 / -1;\n","}\n","\n","dl.xr-attrs {\n","  padding: 0;\n","  margin: 0;\n","  display: grid;\n","  grid-template-columns: 125px auto;\n","}\n","\n",".xr-attrs dt,\n",".xr-attrs dd {\n","  padding: 0;\n","  margin: 0;\n","  float: left;\n","  padding-right: 10px;\n","  width: auto;\n","}\n","\n",".xr-attrs dt {\n","  font-weight: normal;\n","  grid-column: 1;\n","}\n","\n",".xr-attrs dt:hover span {\n","  display: inline-block;\n","  background: var(--xr-background-color);\n","  padding-right: 10px;\n","}\n","\n",".xr-attrs dd {\n","  grid-column: 2;\n","  white-space: pre-wrap;\n","  word-break: break-all;\n","}\n","\n",".xr-icon-database,\n",".xr-icon-file-text2,\n",".xr-no-icon {\n","  display: inline-block;\n","  vertical-align: middle;\n","  width: 1em;\n","  height: 1.5em !important;\n","  stroke-width: 0;\n","  stroke: currentColor;\n","  fill: currentColor;\n","}\n","</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n","Dimensions:  (y_dim_0: 6905)\n","Coordinates:\n","  * y_dim_0  (y_dim_0) int64 0 1 2 3 4 5 6 ... 6899 6900 6901 6902 6903 6904\n","Data variables:\n","    y        (y_dim_0) float64 -0.3667 -0.9172 -0.2576 ... 0.3408 -0.1191 0.6071\n","Attributes:\n","    created_at:                 2023-09-17T02:55:38.535667\n","    arviz_version:              0.14.0\n","    inference_library:          pymc\n","    inference_library_version:  5.6.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-071e9c41-6fbe-45ef-a664-93c65c92fb60' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-071e9c41-6fbe-45ef-a664-93c65c92fb60' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>y_dim_0</span>: 6905</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-da5dd8f3-94b7-4f35-8964-72dac1e83897' class='xr-section-summary-in' type='checkbox'  checked><label for='section-da5dd8f3-94b7-4f35-8964-72dac1e83897' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>y_dim_0</span></div><div class='xr-var-dims'>(y_dim_0)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 6901 6902 6903 6904</div><input id='attrs-0696028f-0d5b-49c4-8d1d-d570a08f8b34' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-0696028f-0d5b-49c4-8d1d-d570a08f8b34' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-adc451d4-cdf9-487c-b981-2493bcd5e746' class='xr-var-data-in' type='checkbox'><label for='data-adc451d4-cdf9-487c-b981-2493bcd5e746' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 6902, 6903, 6904])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-1063c4cf-8851-4a3a-85f9-7ada45aeaf33' class='xr-section-summary-in' type='checkbox'  checked><label for='section-1063c4cf-8851-4a3a-85f9-7ada45aeaf33' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>y</span></div><div class='xr-var-dims'>(y_dim_0)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-0.3667 -0.9172 ... -0.1191 0.6071</div><input id='attrs-140456ae-d937-4891-81e3-5f03487e8081' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-140456ae-d937-4891-81e3-5f03487e8081' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-5ea3564b-a1e9-4d2f-902f-fdc1b4f631aa' class='xr-var-data-in' type='checkbox'><label for='data-5ea3564b-a1e9-4d2f-902f-fdc1b4f631aa' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([-0.36673852, -0.91717184, -0.25759692, ...,  0.34081092,\n","       -0.11906557,  0.6070664 ])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-44369ec1-ca86-477c-affe-6e05e558c6c2' class='xr-section-summary-in' type='checkbox'  ><label for='section-44369ec1-ca86-477c-affe-6e05e558c6c2' class='xr-section-summary' >Indexes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>y_dim_0</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-3245402d-e4ae-4ee6-876a-2305386f10ff' class='xr-index-data-in' type='checkbox'/><label for='index-3245402d-e4ae-4ee6-876a-2305386f10ff' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,\n","            ...\n","            6895, 6896, 6897, 6898, 6899, 6900, 6901, 6902, 6903, 6904],\n","           dtype=&#x27;int64&#x27;, name=&#x27;y_dim_0&#x27;, length=6905))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-e955789d-814c-48b5-a285-7d9d21613896' class='xr-section-summary-in' type='checkbox'  checked><label for='section-e955789d-814c-48b5-a285-7d9d21613896' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-09-17T02:55:38.535667</dd><dt><span>arviz_version :</span></dt><dd>0.14.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.0</dd></dl></div></li></ul></div></div><br></div>\n","                      </ul>\n","                  </div>\n","            </li>\n","            \n","            <li class = \"xr-section-item\">\n","                  <input id=\"idata_constant_datade3ce9e5-7a74-45cf-b2d8-f51dc5a90205\" class=\"xr-section-summary-in\" type=\"checkbox\">\n","                  <label for=\"idata_constant_datade3ce9e5-7a74-45cf-b2d8-f51dc5a90205\" class = \"xr-section-summary\">constant_data</label>\n","                  <div class=\"xr-section-inline-details\"></div>\n","                  <div class=\"xr-section-details\">\n","                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n","                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n","<defs>\n","<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n","<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n","<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n","<path d=\"M16 26c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n","</symbol>\n","<symbol id=\"icon-file-text2\" viewBox=\"0 0 32 32\">\n","<path d=\"M28.681 7.159c-0.694-0.947-1.662-2.053-2.724-3.116s-2.169-2.030-3.116-2.724c-1.612-1.182-2.393-1.319-2.841-1.319h-15.5c-1.378 0-2.5 1.121-2.5 2.5v27c0 1.378 1.122 2.5 2.5 2.5h23c1.378 0 2.5-1.122 2.5-2.5v-19.5c0-0.448-0.137-1.23-1.319-2.841zM24.543 5.457c0.959 0.959 1.712 1.825 2.268 2.543h-4.811v-4.811c0.718 0.556 1.584 1.309 2.543 2.268zM28 29.5c0 0.271-0.229 0.5-0.5 0.5h-23c-0.271 0-0.5-0.229-0.5-0.5v-27c0-0.271 0.229-0.5 0.5-0.5 0 0 15.499-0 15.5 0v7c0 0.552 0.448 1 1 1h7v19.5z\"></path>\n","<path d=\"M23 26h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n","<path d=\"M23 22h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n","<path d=\"M23 18h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n","</symbol>\n","</defs>\n","</svg>\n","<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n"," *\n"," */\n","\n",":root {\n","  --xr-font-color0: var(--jp-content-font-color0, 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min-width: 300px;\n","  max-width: 700px;\n","}\n","\n",".xr-text-repr-fallback {\n","  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n","  display: none;\n","}\n","\n",".xr-header {\n","  padding-top: 6px;\n","  padding-bottom: 6px;\n","  margin-bottom: 4px;\n","  border-bottom: solid 1px var(--xr-border-color);\n","}\n","\n",".xr-header > div,\n",".xr-header > ul {\n","  display: inline;\n","  margin-top: 0;\n","  margin-bottom: 0;\n","}\n","\n",".xr-obj-type,\n",".xr-array-name {\n","  margin-left: 2px;\n","  margin-right: 10px;\n","}\n","\n",".xr-obj-type {\n","  color: var(--xr-font-color2);\n","}\n","\n",".xr-sections {\n","  padding-left: 0 !important;\n","  display: grid;\n","  grid-template-columns: 150px auto auto 1fr 20px 20px;\n","}\n","\n",".xr-section-item {\n","  display: contents;\n","}\n","\n",".xr-section-item input {\n","  display: none;\n","}\n","\n",".xr-section-item input + label {\n","  color: var(--xr-disabled-color);\n","}\n","\n",".xr-section-item input:enabled + label {\n","  cursor: pointer;\n","  color: var(--xr-font-color2);\n","}\n","\n",".xr-section-item input:enabled + label:hover {\n","  color: var(--xr-font-color0);\n","}\n","\n",".xr-section-summary {\n","  grid-column: 1;\n","  color: var(--xr-font-color2);\n","  font-weight: 500;\n","}\n","\n",".xr-section-summary > span {\n","  display: inline-block;\n","  padding-left: 0.5em;\n","}\n","\n",".xr-section-summary-in:disabled + label {\n","  color: var(--xr-font-color2);\n","}\n","\n",".xr-section-summary-in + label:before {\n","  display: inline-block;\n","  content: '►';\n","  font-size: 11px;\n","  width: 15px;\n","  text-align: center;\n","}\n","\n",".xr-section-summary-in:disabled + label:before {\n","  color: var(--xr-disabled-color);\n","}\n","\n",".xr-section-summary-in:checked + label:before {\n","  content: '▼';\n","}\n","\n",".xr-section-summary-in:checked + label > span {\n","  display: none;\n","}\n","\n",".xr-section-summary,\n",".xr-section-inline-details {\n","  padding-top: 4px;\n","  padding-bottom: 4px;\n","}\n","\n",".xr-section-inline-details {\n","  grid-column: 2 / -1;\n","}\n","\n",".xr-section-details {\n","  display: none;\n","  grid-column: 1 / -1;\n","  margin-bottom: 5px;\n","}\n","\n",".xr-section-summary-in:checked ~ .xr-section-details {\n","  display: contents;\n","}\n","\n",".xr-array-wrap {\n","  grid-column: 1 / -1;\n","  display: grid;\n","  grid-template-columns: 20px auto;\n","}\n","\n",".xr-array-wrap > label {\n","  grid-column: 1;\n","  vertical-align: top;\n","}\n","\n",".xr-preview {\n","  color: var(--xr-font-color3);\n","}\n","\n",".xr-array-preview,\n",".xr-array-data {\n","  padding: 0 5px !important;\n","  grid-column: 2;\n","}\n","\n",".xr-array-data,\n",".xr-array-in:checked ~ .xr-array-preview {\n","  display: none;\n","}\n","\n",".xr-array-in:checked ~ .xr-array-data,\n",".xr-array-preview {\n","  display: inline-block;\n","}\n","\n",".xr-dim-list {\n","  display: inline-block !important;\n","  list-style: none;\n","  padding: 0 !important;\n","  margin: 0;\n","}\n","\n",".xr-dim-list li {\n","  display: inline-block;\n","  padding: 0;\n","  margin: 0;\n","}\n","\n",".xr-dim-list:before {\n","  content: '(';\n","}\n","\n",".xr-dim-list:after {\n","  content: ')';\n","}\n","\n",".xr-dim-list li:not(:last-child):after {\n","  content: ',';\n","  padding-right: 5px;\n","}\n","\n",".xr-has-index {\n","  font-weight: bold;\n","}\n","\n",".xr-var-list,\n",".xr-var-item {\n","  display: contents;\n","}\n","\n",".xr-var-item > div,\n",".xr-var-item label,\n",".xr-var-item > .xr-var-name span {\n","  background-color: var(--xr-background-color-row-even);\n","  margin-bottom: 0;\n","}\n","\n",".xr-var-item > .xr-var-name:hover span {\n","  padding-right: 5px;\n","}\n","\n",".xr-var-list > li:nth-child(odd) > div,\n",".xr-var-list > li:nth-child(odd) > label,\n",".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n","  background-color: var(--xr-background-color-row-odd);\n","}\n","\n",".xr-var-name {\n","  grid-column: 1;\n","}\n","\n",".xr-var-dims {\n","  grid-column: 2;\n","}\n","\n",".xr-var-dtype {\n","  grid-column: 3;\n","  text-align: right;\n","  color: var(--xr-font-color2);\n","}\n","\n",".xr-var-preview {\n","  grid-column: 4;\n","}\n","\n",".xr-index-preview {\n","  grid-column: 2 / 5;\n","  color: var(--xr-font-color2);\n","}\n","\n",".xr-var-name,\n",".xr-var-dims,\n",".xr-var-dtype,\n",".xr-preview,\n",".xr-attrs dt {\n","  white-space: nowrap;\n","  overflow: hidden;\n","  text-overflow: ellipsis;\n","  padding-right: 10px;\n","}\n","\n",".xr-var-name:hover,\n",".xr-var-dims:hover,\n",".xr-var-dtype:hover,\n",".xr-attrs dt:hover {\n","  overflow: visible;\n","  width: auto;\n","  z-index: 1;\n","}\n","\n",".xr-var-attrs,\n",".xr-var-data,\n",".xr-index-data {\n","  display: none;\n","  background-color: var(--xr-background-color) !important;\n","  padding-bottom: 5px !important;\n","}\n","\n",".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",".xr-var-data-in:checked ~ .xr-var-data,\n",".xr-index-data-in:checked ~ .xr-index-data {\n","  display: block;\n","}\n","\n",".xr-var-data > table {\n","  float: right;\n","}\n","\n",".xr-var-name span,\n",".xr-var-data,\n",".xr-index-name div,\n",".xr-index-data,\n",".xr-attrs {\n","  padding-left: 25px !important;\n","}\n","\n",".xr-attrs,\n",".xr-var-attrs,\n",".xr-var-data,\n",".xr-index-data {\n","  grid-column: 1 / -1;\n","}\n","\n","dl.xr-attrs {\n","  padding: 0;\n","  margin: 0;\n","  display: grid;\n","  grid-template-columns: 125px auto;\n","}\n","\n",".xr-attrs dt,\n",".xr-attrs dd {\n","  padding: 0;\n","  margin: 0;\n","  float: left;\n","  padding-right: 10px;\n","  width: auto;\n","}\n","\n",".xr-attrs dt {\n","  font-weight: normal;\n","  grid-column: 1;\n","}\n","\n",".xr-attrs dt:hover span {\n","  display: inline-block;\n","  background: var(--xr-background-color);\n","  padding-right: 10px;\n","}\n","\n",".xr-attrs dd {\n","  grid-column: 2;\n","  white-space: pre-wrap;\n","  word-break: break-all;\n","}\n","\n",".xr-icon-database,\n",".xr-icon-file-text2,\n",".xr-no-icon {\n","  display: inline-block;\n","  vertical-align: middle;\n","  width: 1em;\n","  height: 1.5em !important;\n","  stroke-width: 0;\n","  stroke: currentColor;\n","  fill: currentColor;\n","}\n","</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n","Dimensions:  (x_dim_0: 6905)\n","Coordinates:\n","  * x_dim_0  (x_dim_0) int64 0 1 2 3 4 5 6 ... 6899 6900 6901 6902 6903 6904\n","Data variables:\n","    x        (x_dim_0) int32 0 0 0 0 0 0 0 0 0 0 0 0 ... 1 1 1 1 1 1 1 1 1 1 1 1\n","Attributes:\n","    created_at:                 2023-09-17T02:55:38.536475\n","    arviz_version:              0.14.0\n","    inference_library:          pymc\n","    inference_library_version:  5.6.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-b7ef3b8d-77fe-4fbf-b7eb-15b66aae57bb' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-b7ef3b8d-77fe-4fbf-b7eb-15b66aae57bb' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>x_dim_0</span>: 6905</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-dd706782-58a1-4490-a165-6525ee151678' class='xr-section-summary-in' type='checkbox'  checked><label for='section-dd706782-58a1-4490-a165-6525ee151678' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x_dim_0</span></div><div class='xr-var-dims'>(x_dim_0)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 6901 6902 6903 6904</div><input id='attrs-4ac7553f-45c4-4dba-93b0-9a2b75a4413e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-4ac7553f-45c4-4dba-93b0-9a2b75a4413e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-e3f27e76-4277-475a-a701-80b6ef66fb78' class='xr-var-data-in' type='checkbox'><label for='data-e3f27e76-4277-475a-a701-80b6ef66fb78' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 6902, 6903, 6904])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-ae4385fa-5e28-413f-9e87-4985827d24d5' class='xr-section-summary-in' type='checkbox'  checked><label for='section-ae4385fa-5e28-413f-9e87-4985827d24d5' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>x</span></div><div class='xr-var-dims'>(x_dim_0)</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>0 0 0 0 0 0 0 0 ... 1 1 1 1 1 1 1 1</div><input id='attrs-67f02316-a8a3-4b05-81ce-1a47265d3893' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-67f02316-a8a3-4b05-81ce-1a47265d3893' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-89f732fb-9699-4ec3-8d71-ec35119a1dc3' class='xr-var-data-in' type='checkbox'><label for='data-89f732fb-9699-4ec3-8d71-ec35119a1dc3' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 0, 0, ..., 1, 1, 1], dtype=int32)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-54a2b990-6009-4955-94b3-0a3828f0d3f7' class='xr-section-summary-in' type='checkbox'  ><label for='section-54a2b990-6009-4955-94b3-0a3828f0d3f7' class='xr-section-summary' >Indexes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>x_dim_0</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-9abe981d-73af-447c-b01a-2a0d0eaca4e5' class='xr-index-data-in' type='checkbox'/><label for='index-9abe981d-73af-447c-b01a-2a0d0eaca4e5' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,\n","            ...\n","            6895, 6896, 6897, 6898, 6899, 6900, 6901, 6902, 6903, 6904],\n","           dtype=&#x27;int64&#x27;, name=&#x27;x_dim_0&#x27;, length=6905))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-98f9d8e8-5012-4079-8fc6-e7bad8ffc94e' class='xr-section-summary-in' type='checkbox'  checked><label for='section-98f9d8e8-5012-4079-8fc6-e7bad8ffc94e' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-09-17T02:55:38.536475</dd><dt><span>arviz_version :</span></dt><dd>0.14.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.0</dd></dl></div></li></ul></div></div><br></div>\n","                      </ul>\n","                  </div>\n","            </li>\n","            \n","            <li class = \"xr-section-item\">\n","                  <input id=\"idata_predictions_constant_data236cb2b9-f14e-4b6b-9dbf-fc9ad8e87676\" class=\"xr-section-summary-in\" type=\"checkbox\">\n","                  <label for=\"idata_predictions_constant_data236cb2b9-f14e-4b6b-9dbf-fc9ad8e87676\" class = \"xr-section-summary\">predictions_constant_data</label>\n","                  <div class=\"xr-section-inline-details\"></div>\n","                  <div class=\"xr-section-details\">\n","                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n","                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n","<defs>\n","<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n","<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n","<path d=\"M16 17c-8.837 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1z\"></path>\n","<path d=\"M23 18h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n","</symbol>\n","</defs>\n","</svg>\n","<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n"," *\n"," */\n","\n",":root {\n","  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n","  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n","  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n","  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n","  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n","  --xr-background-color: var(--jp-layout-color0, white);\n","  --xr-background-color-row-even: var(--jp-layout-color1, white);\n","  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n","}\n","\n","html[theme=dark],\n","body[data-theme=dark],\n","body.vscode-dark {\n","  --xr-font-color0: rgba(255, 255, 255, 1);\n","  --xr-font-color2: rgba(255, 255, 255, 0.54);\n","  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!important;\n","  display: grid;\n","  grid-template-columns: 150px auto auto 1fr 20px 20px;\n","}\n","\n",".xr-section-item {\n","  display: contents;\n","}\n","\n",".xr-section-item input {\n","  display: none;\n","}\n","\n",".xr-section-item input + label {\n","  color: var(--xr-disabled-color);\n","}\n","\n",".xr-section-item input:enabled + label {\n","  cursor: pointer;\n","  color: var(--xr-font-color2);\n","}\n","\n",".xr-section-item input:enabled + label:hover {\n","  color: var(--xr-font-color0);\n","}\n","\n",".xr-section-summary {\n","  grid-column: 1;\n","  color: var(--xr-font-color2);\n","  font-weight: 500;\n","}\n","\n",".xr-section-summary > span {\n","  display: inline-block;\n","  padding-left: 0.5em;\n","}\n","\n",".xr-section-summary-in:disabled + label {\n","  color: var(--xr-font-color2);\n","}\n","\n",".xr-section-summary-in + label:before {\n","  display: inline-block;\n","  content: '►';\n","  font-size: 11px;\n","  width: 15px;\n","  text-align: center;\n","}\n","\n",".xr-section-summary-in:disabled + label:before {\n","  color: var(--xr-disabled-color);\n","}\n","\n",".xr-section-summary-in:checked + label:before {\n","  content: '▼';\n","}\n","\n",".xr-section-summary-in:checked + label > span {\n","  display: none;\n","}\n","\n",".xr-section-summary,\n",".xr-section-inline-details {\n","  padding-top: 4px;\n","  padding-bottom: 4px;\n","}\n","\n",".xr-section-inline-details {\n","  grid-column: 2 / -1;\n","}\n","\n",".xr-section-details {\n","  display: none;\n","  grid-column: 1 / -1;\n","  margin-bottom: 5px;\n","}\n","\n",".xr-section-summary-in:checked ~ .xr-section-details {\n","  display: contents;\n","}\n","\n",".xr-array-wrap {\n","  grid-column: 1 / -1;\n","  display: grid;\n","  grid-template-columns: 20px auto;\n","}\n","\n",".xr-array-wrap > label {\n","  grid-column: 1;\n","  vertical-align: top;\n","}\n","\n",".xr-preview {\n","  color: var(--xr-font-color3);\n","}\n","\n",".xr-array-preview,\n",".xr-array-data {\n","  padding: 0 5px !important;\n","  grid-column: 2;\n","}\n","\n",".xr-array-data,\n",".xr-array-in:checked ~ .xr-array-preview {\n","  display: none;\n","}\n","\n",".xr-array-in:checked ~ .xr-array-data,\n",".xr-array-preview {\n","  display: inline-block;\n","}\n","\n",".xr-dim-list {\n","  display: inline-block !important;\n","  list-style: none;\n","  padding: 0 !important;\n","  margin: 0;\n","}\n","\n",".xr-dim-list li {\n","  display: inline-block;\n","  padding: 0;\n","  margin: 0;\n","}\n","\n",".xr-dim-list:before {\n","  content: '(';\n","}\n","\n",".xr-dim-list:after {\n","  content: ')';\n","}\n","\n",".xr-dim-list li:not(:last-child):after {\n","  content: ',';\n","  padding-right: 5px;\n","}\n","\n",".xr-has-index {\n","  font-weight: bold;\n","}\n","\n",".xr-var-list,\n",".xr-var-item {\n","  display: contents;\n","}\n","\n",".xr-var-item > div,\n",".xr-var-item label,\n",".xr-var-item > .xr-var-name span {\n","  background-color: var(--xr-background-color-row-even);\n","  margin-bottom: 0;\n","}\n","\n",".xr-var-item > .xr-var-name:hover span {\n","  padding-right: 5px;\n","}\n","\n",".xr-var-list > li:nth-child(odd) > div,\n",".xr-var-list > li:nth-child(odd) > label,\n",".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n","  background-color: var(--xr-background-color-row-odd);\n","}\n","\n",".xr-var-name {\n","  grid-column: 1;\n","}\n","\n",".xr-var-dims {\n","  grid-column: 2;\n","}\n","\n",".xr-var-dtype {\n","  grid-column: 3;\n","  text-align: right;\n","  color: var(--xr-font-color2);\n","}\n","\n",".xr-var-preview {\n","  grid-column: 4;\n","}\n","\n",".xr-index-preview {\n","  grid-column: 2 / 5;\n","  color: var(--xr-font-color2);\n","}\n","\n",".xr-var-name,\n",".xr-var-dims,\n",".xr-var-dtype,\n",".xr-preview,\n",".xr-attrs dt {\n","  white-space: nowrap;\n","  overflow: hidden;\n","  text-overflow: ellipsis;\n","  padding-right: 10px;\n","}\n","\n",".xr-var-name:hover,\n",".xr-var-dims:hover,\n",".xr-var-dtype:hover,\n",".xr-attrs dt:hover {\n","  overflow: visible;\n","  width: auto;\n","  z-index: 1;\n","}\n","\n",".xr-var-attrs,\n",".xr-var-data,\n",".xr-index-data {\n","  display: none;\n","  background-color: var(--xr-background-color) !important;\n","  padding-bottom: 5px !important;\n","}\n","\n",".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",".xr-var-data-in:checked ~ .xr-var-data,\n",".xr-index-data-in:checked ~ .xr-index-data {\n","  display: block;\n","}\n","\n",".xr-var-data > table {\n","  float: right;\n","}\n","\n",".xr-var-name span,\n",".xr-var-data,\n",".xr-index-name div,\n",".xr-index-data,\n",".xr-attrs {\n","  padding-left: 25px !important;\n","}\n","\n",".xr-attrs,\n",".xr-var-attrs,\n",".xr-var-data,\n",".xr-index-data {\n","  grid-column: 1 / -1;\n","}\n","\n","dl.xr-attrs {\n","  padding: 0;\n","  margin: 0;\n","  display: grid;\n","  grid-template-columns: 125px auto;\n","}\n","\n",".xr-attrs dt,\n",".xr-attrs dd {\n","  padding: 0;\n","  margin: 0;\n","  float: left;\n","  padding-right: 10px;\n","  width: auto;\n","}\n","\n",".xr-attrs dt {\n","  font-weight: normal;\n","  grid-column: 1;\n","}\n","\n",".xr-attrs dt:hover span {\n","  display: inline-block;\n","  background: var(--xr-background-color);\n","  padding-right: 10px;\n","}\n","\n",".xr-attrs dd {\n","  grid-column: 2;\n","  white-space: pre-wrap;\n","  word-break: break-all;\n","}\n","\n",".xr-icon-database,\n",".xr-icon-file-text2,\n",".xr-no-icon {\n","  display: inline-block;\n","  vertical-align: middle;\n","  width: 1em;\n","  height: 1.5em !important;\n","  stroke-width: 0;\n","  stroke: currentColor;\n","  fill: currentColor;\n","}\n","</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n","Dimensions:  (x_dim_0: 6905)\n","Coordinates:\n","  * x_dim_0  (x_dim_0) int64 0 1 2 3 4 5 6 ... 6899 6900 6901 6902 6903 6904\n","Data variables:\n","    x        (x_dim_0) int32 0 0 0 0 0 0 0 0 0 0 0 0 ... 1 1 1 1 1 1 1 1 1 1 1 1\n","Attributes:\n","    created_at:                 2023-09-17T02:55:48.234587\n","    arviz_version:              0.14.0\n","    inference_library:          pymc\n","    inference_library_version:  5.6.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-9a496568-9b9b-4944-84bc-d5d9b895c8a5' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-9a496568-9b9b-4944-84bc-d5d9b895c8a5' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>x_dim_0</span>: 6905</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-43cd420c-024c-475c-8a0d-b86e58eafa41' class='xr-section-summary-in' type='checkbox'  checked><label for='section-43cd420c-024c-475c-8a0d-b86e58eafa41' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x_dim_0</span></div><div class='xr-var-dims'>(x_dim_0)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 6901 6902 6903 6904</div><input id='attrs-a832911b-dc13-4ba4-bf3e-fefbcf65259a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-a832911b-dc13-4ba4-bf3e-fefbcf65259a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-931daed1-d2e8-4fa2-b3e7-f60aed6b3ff8' class='xr-var-data-in' type='checkbox'><label for='data-931daed1-d2e8-4fa2-b3e7-f60aed6b3ff8' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 6902, 6903, 6904])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-c4d761a1-df57-432d-8491-165429045543' class='xr-section-summary-in' type='checkbox'  checked><label for='section-c4d761a1-df57-432d-8491-165429045543' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>x</span></div><div class='xr-var-dims'>(x_dim_0)</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>0 0 0 0 0 0 0 0 ... 1 1 1 1 1 1 1 1</div><input id='attrs-66384188-9227-4eff-9ced-ac21b1b56cdb' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-66384188-9227-4eff-9ced-ac21b1b56cdb' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-e0fd6b66-bdd0-4344-ae7d-ade400fddba8' class='xr-var-data-in' type='checkbox'><label for='data-e0fd6b66-bdd0-4344-ae7d-ade400fddba8' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 0, 0, ..., 1, 1, 1], dtype=int32)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-eee10a99-99b2-4364-a615-e2b5d73c7757' class='xr-section-summary-in' type='checkbox'  ><label for='section-eee10a99-99b2-4364-a615-e2b5d73c7757' class='xr-section-summary' >Indexes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>x_dim_0</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-9c5d0d3a-4415-4cba-bf0b-4d44ca01cada' class='xr-index-data-in' type='checkbox'/><label for='index-9c5d0d3a-4415-4cba-bf0b-4d44ca01cada' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,\n","            ...\n","            6895, 6896, 6897, 6898, 6899, 6900, 6901, 6902, 6903, 6904],\n","           dtype=&#x27;int64&#x27;, name=&#x27;x_dim_0&#x27;, length=6905))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-5c20f594-0d86-4337-bd38-2197a9aebaa4' class='xr-section-summary-in' type='checkbox'  checked><label for='section-5c20f594-0d86-4337-bd38-2197a9aebaa4' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-09-17T02:55:48.234587</dd><dt><span>arviz_version :</span></dt><dd>0.14.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.0</dd></dl></div></li></ul></div></div><br></div>\n","                      </ul>\n","                  </div>\n","            </li>\n","            \n","              </ul>\n","            </div>\n","            <style> /* CSS stylesheet for displaying InferenceData objects in jupyterlab.\n"," *\n"," */\n","\n",":root {\n","  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n","  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n","  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n","  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n","  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n","  --xr-background-color: var(--jp-layout-color0, white);\n","  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predictions_constant_data"]},"execution_count":15,"metadata":{},"output_type":"execute_result"}],"source":["idata_ppc"]},{"cell_type":"code","execution_count":16,"metadata":{"collapsed":false,"id":"1A65BD5E8B664F74BB59B985B1FBC7E9","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[{"data":{"text/html":["<div>\n","<style scoped>\n","    .dataframe tbody tr th:only-of-type {\n","        vertical-align: middle;\n","    }\n","\n","    .dataframe tbody tr th {\n","        vertical-align: top;\n","    }\n","\n","    .dataframe thead th {\n","        text-align: right;\n","    }\n","</style>\n","<table border=\"1\" class=\"dataframe\">\n","  <thead>\n","    <tr style=\"text-align: right;\">\n","      <th></th>\n","      <th>x</th>\n","      <th>y_mean</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>0</th>\n","      <td>0</td>\n","      <td>-0.015016</td>\n","    </tr>\n","    <tr>\n","      <th>1</th>\n","      <td>0</td>\n","      <td>-0.016379</td>\n","    </tr>\n","    <tr>\n","      <th>2</th>\n","      <td>0</td>\n","      <td>-0.006570</td>\n","    </tr>\n","    <tr>\n","      <th>3</th>\n","      <td>0</td>\n","      <td>-0.028285</td>\n","    </tr>\n","    <tr>\n","      <th>4</th>\n","      <td>0</td>\n","      <td>-0.018867</td>\n","    </tr>\n","    <tr>\n","      <th>...</th>\n","      <td>...</td>\n","      <td>...</td>\n","    </tr>\n","    <tr>\n","      <th>6900</th>\n","      <td>1</td>\n","      <td>0.006583</td>\n","    </tr>\n","    <tr>\n","      <th>6901</th>\n","      <td>1</td>\n","      <td>0.027325</td>\n","    </tr>\n","    <tr>\n","      <th>6902</th>\n","      <td>1</td>\n","      <td>0.006328</td>\n","    </tr>\n","    <tr>\n","      <th>6903</th>\n","      <td>1</td>\n","      <td>0.017191</td>\n","    </tr>\n","    <tr>\n","      <th>6904</th>\n","      <td>1</td>\n","      <td>0.002549</td>\n","    </tr>\n","  </tbody>\n","</table>\n","<p>6905 rows × 2 columns</p>\n","</div>"],"text/plain":["      x    y_mean\n","0     0 -0.015016\n","1     0 -0.016379\n","2     0 -0.006570\n","3     0 -0.028285\n","4     0 -0.018867\n","...  ..       ...\n","6900  1  0.006583\n","6901  1  0.027325\n","6902  1  0.006328\n","6903  1  0.017191\n","6904  1  0.002549\n","\n","[6905 rows x 2 columns]"]},"execution_count":16,"metadata":{},"output_type":"execute_result"}],"source":["df_ppc = pd.DataFrame({\n","    \"x\": idata_ppc.constant_data.x.values, \n","    \"y_mean\": idata_ppc.predictions.y.mean([\"chain\", \"draw\"]).values # 合并 chains 和 draw 为均值\n","})\n","df_ppc"]},{"cell_type":"code","execution_count":17,"metadata":{"collapsed":false,"id":"9CBEDEA7BD5240A5BFD1FC880F7ED408","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[{"data":{"text/plain":["array([0.01355639, 0.01519054, 0.01070339, ..., 0.00632784, 0.01719058,\n","       0.00254927])"]},"execution_count":17,"metadata":{},"output_type":"execute_result"}],"source":["df_ppc[df_ppc.x==1].y_mean.values"]},{"cell_type":"code","execution_count":18,"metadata":{"_id":"F13551FB525D42AF84F837BFFA58923E","collapsed":false,"id":"CF5B66E04A004D7486251C4DA6D773E9","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[{"name":"stderr","output_type":"stream","text":["/tmp/ipykernel_81/3477623782.py:24: UserWarning: The figure layout has changed to tight\n","  fig.tight_layout()\n"]},{"data":{"text/html":["<img src=\"https://cdn.kesci.com/upload/rt/CF5B66E04A004D7486251C4DA6D773E9/s1405respt.png\">"],"text/plain":["<Figure size 400x300 with 1 Axes>"]},"metadata":{"image/png":{"height":311,"width":411}},"output_type":"display_data"}],"source":["labels = ['低', '高']\n","obs_low = SMS_data.query('factor==\"Low\"').variable\n","obs_high = SMS_data.query('factor==\"High\"').variable\n","ppc_low = df_ppc[df_ppc.x==1].y_mean.values\n","ppc_high = df_ppc[df_ppc.x==0].y_mean.values\n","\n","fig, ax = plt.subplots()\n","part1 = ax.violinplot(\n","    [list(obs_low),list(obs_high)], \n","    [1,4], points=100, widths=0.3, \n","    showmeans=True, showextrema=True, showmedians=True)\n","part2 = ax.violinplot(\n","    [list(ppc_low),list(ppc_high)], \n","    [2,5], points=100, widths=0.3, \n","    showmeans=True, showextrema=True, showmedians=True)\n","part1['bodies'][0].set_label('观测数据')\n","part2['bodies'][0].set_label('预测数据')\n","# Add some text for labels, title and custom x-axis tick labels, etc.\n","ax.set_ylabel('幸福感')\n","ax.set_title('Posterior predictive check')\n","plt.xticks([1.5,4.5], labels)\n","ax.legend()\n","\n","fig.tight_layout()\n","plt.show()"]},{"cell_type":"markdown","metadata":{"_id":"D19B293109B740B3B713B8FB8C46AB28","id":"1C4AD47D99974ECEB7B284627A2E4735","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["### 例2: 贝叶斯推断在认知模型中的应用"]},{"cell_type":"markdown","metadata":{"_id":"646D4BFEAD8748C9887E33AE4310081C","id":"7F2AEF05CCCD4A5AB2D9F31454D9F3BA","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["在实验数据的收集时，研究者往往会采集个体反应的正确率与反应时。  \n","\n","而传统分析方法并不能同时对两种数据进行分析，从而推断潜在的认知机制。比如，个体是否愿意牺牲更多的反应时间去获得一个更准确的判断。  \n","\n","认知模型能有效的弥补这一问题，比如 drift-diffusion model, DDM。"]},{"cell_type":"markdown","metadata":{"_id":"B585B1C93AF5443F8CA4463DC16B0820","id":"8529BF553A6F4098BF2DDC7F1639D442","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["\n","![DDM1](https://cdn.kesci.com/upload/image/rhb2957an5.png?imageView2/0/w/960/h/960)  \n"]},{"cell_type":"markdown","metadata":{"_id":"18059BD0671147DB88E3010DF8822F6B","id":"82323D9E9C1A49F28914A82819A1A058","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["<div style=\"text-align: center;\">\t \n","\t\n","## Part 3: About this course  \n","\t\n","</div> "]},{"cell_type":"markdown","metadata":{"_id":"5D1D738B647048C98E03422D6C00D151","id":"3A806EA51D58404A90C57C4AC3034E7D","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["# 2. 课程内容  \n","### 2.0 课时  \n","9.05 ～ 12.30，18周，十一假期可能会被放假一次  \n","\n","### 2.1 教学目标：  \n","\n","（1）使用Python进行基本的数据处理  \n","\n","（2）理解贝叶斯推断的基本原理；  \n","\n","（2）了解PyMC3的语法和结构，并能应用于相对简单的情境  "]},{"cell_type":"markdown","metadata":{"_id":"A9F58FE9AFBA479C8E5CFE414F37F734","id":"7B848BDF204E49DCADFC62B32BC43BDC","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["\n","### 2.2 考核方式：  \n","\n","#### 考勤  \n","10%  \n","\n","\n"]},{"cell_type":"markdown","metadata":{"_id":"445A3A97ABA44BC188AC4E33A9963653","id":"4A4ADEE653A3460F9CC7321D924CF304","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["#### 小作业 (45%)  \n","\t\n","（1）使用numpy与pandas进行基本的数据预处理；  \n","\n","（2）使用pymc对随机变量进行简单线性回归模型的建模；  \n","\n","（3）使用arviz进行统计推断。"]},{"cell_type":"markdown","metadata":{"_id":"ECB7C0A67BDE4862B4286D8BF5EB8D56","id":"BEB6F3227BEB4BF89B11C61E5E287B11","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["#### 大作业 (45%)   \n","真实的数据分析  \n","* 合作完成  \n","* 包括代码与文字报告  \n","* 进行汇报  \n","* 标准：分工合理、数据分析流程完整、汇报展示清晰美观"]},{"cell_type":"markdown","metadata":{"_id":"E5E0F67166074C378C6B5E5AC1DE367F","id":"789D0E1F45FE4DA0A5415EAA7AA3C057","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["\n","### 2.3 课程风格：  \n","\t（1）内容有挑战、考核不复杂  \n","\t（2）1/3一节课展示或互动抄代码  \n","\t（3）专门设有答疑时间，助教给大家答疑解惑  \n","\n","\n"]},{"cell_type":"markdown","metadata":{"_id":"12247097A60245CD8ACED2542DAF006E","id":"BF9BAA4384914133AF8E7A4CC89B8729","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["\n","### 2.4 课程大纲  \n","### Intro  \n","1: 课程介绍（为什么要用贝叶斯/PyMC3，展示一个回归分析例子，课程安排）  \n","\n","### I Basics：  \n","2: 贝叶斯公式  \n","* 单一事件的贝叶斯模型(先验、似然、分母和后验)  \n","* 随机变量的贝叶斯模型(先验、似然、分母和后验)  \n","\n","3: 建立一个完成的贝叶斯模型：Beta-Binomial model  \n","* Beta先验  \n","* Binomial与似然  \n","* Beta-Binomial model  \n","\n","4: 贝叶斯模型的特点：数据-先验与动态更新  \n","* 先验与数据对后验的影响  \n","* 数据顺序不影响后验  \n","\n","5: 经典的贝叶斯模型：Conjugate families  \n","* Gamma-Poisson  \n","* Normal-Normal  \n","\n","### II 近似后验估计  \n","6: 近似后验的方法  \n","* 网格法  \n","* MCMC  \n","\n","7: 深入一种MCMC算法  \n","* M-H 算法  \n","\n","8: 基于后验的推断  \n","* 后验估计  \n","* 假设检验  \n","* 后验预没  \n","\n","### III Bayesian回归模型  \n","9: 简单的Bayesian线性回归模型  \n","* 建立模型  \n","* 调整先验  \n","* 近似后验  \n","* 基于近似后验的推断  \n","* 序列分析  \n","\n","10: 对回归模型的评估  \n","* 评估模型的标准  \n","* 对简单线性模型的估计  \n","  \n","11: 扩散线性模型  \n","* 多自变量的线性回归  \n","\n","12: GLM: Possion & Negative Binomial Regression  \n","\n","13: GLM: Logistic Regression  \n","\n","14: GLM: Naive Bayes Classification  \n","\n","15: Hierachical Bayesian Model"]},{"cell_type":"markdown","metadata":{"_id":"C46D510264A041FFBF0D926E3A741D6D","id":"7BB9BC5BF1B84FF18BF3C21C8211A425","jupyter":{},"notebookId":"6503d223f8b7cce3ba23ec6e","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["### 2.5 参考书  \n","\n","<div style=\"display: flex;\">  \n","\t<img src=\"https://cdn.kesci.com/upload/s0i1y2dj22.jpeg?imageView2/0/w/320/h/320\" alt=\"BayesRule\" style=\"flex: 1;\">  \n","\t<img src=\"https://cdn.kesci.com/upload/s0i1xtsmcj.jpg?imageView2/0/w/320/h/320\" alt=\"BayesianInPython\" style=\"flex: 1;\">  \n","  <img src=\"https://cdn.kesci.com/upload/s0i1xcemfe.png?imageView2/0/w/320/h/320\" alt=\"StatsRethinking\" style=\"flex: 1;\">  \n","\t<img src=\"https://cdn.kesci.com/upload/s0i26ml0bk.jpg?imageView2/0/w/320/h/320\" alt=\"StudentGuide\" style=\"flex: 1;\">  \n","</div>"]}],"metadata":{"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.5.2"}},"nbformat":4,"nbformat_minor":2}
